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3. Under reasonable hypotheses, what will be the derivative of the product fgh of three functions?...
21. Find the derivative of each of the following functions by applying the product rule a....
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
3. (5 pts) For each of the listed functions, determine a formula for the derivative function....
3. (5 pts) For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter three, use the limit definition, Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than f and r. For...
3. Find the derivative of the following functions: (6 points) (a) x2y2- 10 = xey -...
3. Find the derivative of the following functions: (6 points) (a) x2y2- 10 = xey - 10x (b) x*(x+y) y3 (3x - y) (c) yex ycos(x2) dx 17 A is leaning aoainst a wall and sliding towards the floo
3. Find the derivative of the following functions: (6 points) (a) x2y2- 10 = xey - 10x (b) x*(x+y) y3 (3x - y) (c) yex ycos(x2) dx 17 A is leaning aoainst a wall and sliding towards the floo
4. Consider functions
4. Consider functions \(f(x, y)=\sqrt[3]{x^{3}+y^{3}}\) and \(\mathbf{c}(t)=(t, 2 t)\).(a) Show that \(f_{x}(0,0)\) and \(f_{y}(0,0)\) exist. What is \(\nabla f(0,0)\) ?(b) Show that \(f\) is not differentiable at the point \((0,0)\).(c) Find \((f \circ c)(t)\) and then compute its derivative at the point \(t=0\).(d) Show that \((f \circ \mathbf{c})^{\prime}(0) \neq \nabla f(\mathbf{c}(0)) \cdot \mathbf{c}^{\prime}(0)\). Does this contradict the chain rule formula? why? why not?
Question 1. Compute the derivative of the following functions.
Question 1. Compute the derivative of the following functions.(a) \(f(x)=x^{3}-\frac{2}{\sqrt{x}}+4\)(b) \(f(x)=2^{3 x-1}\)(c) \(f(x)=\ln \left(5 x^{2}+1\right)\)(d) \(f(x)=\frac{\tan (x)}{x^{2}+1}\)(e) \(f(x)=e^{x^{2}} \cdot \arctan (2 x)\)(f) \(f(x)=\sin (x)^{2} \cdot\left(\tan (x)+\cos (x)^{2}\right)\).Question 2. In geometry, the folium of Descartes is a curve given by the equation$$ x^{3}+y^{3}-3 a x y=0 $$Here, \(a\) is a constant.The curve was first proposed by Descartes in 1638 . Its claim to fame lies in an incident in the development of calculus. Descartes challenged Fermat to find the tangent line...
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values...
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values of f' are given in the table above. It is known that f(0) = 3. (a) For f'(x), the conditions of the Mean Value Theorem are met on the closed interval (0,3). The conclusion of the Mean Value Theorem over the interval (0,3) for f'(x) is satisfied at c = 1. Find f"(c). (b) Use a right Riemann sum with the three subintervals indicated...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
(1 point) Functions of the form f(x)= x, where n= 1,2, 3.., are often called power...
(1 point) Functions of the form f(x)= x, where n= 1,2, 3.., are often called power functions (a) Use the limit definition of the derivative to find f'() for f(x)x. fx) (b) Use the limit definition of the derivative to find f '(x) for f(x) = f'(x) (c) Use the limit definition of the derivative to find f'(x) for f(x) = x.(Hint : (a + b) +4ab +b. Apply this rule to (x + h a +4ab+6a b within the...
real analysis 1,2,3,4,8please 5.1.5a Thus iff: I→R is differentiable on n E N. is differentiable on / with g'...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
question - 4 plzzzzzzzzzzz draw the graph !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1. Find the derivative of each of the...
question - 4 plzzzzzzzzzzz draw the
graph
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Find the derivative of each of the following unctions: (e) w- 4u/2 (f) w=4u1/4 12 (c) y7x (b) y 63 2, Find the following: 0 (b) -9x1/3 (-oub du 3. Find f(1) and f(2) from the following functions: (C) f(x)--5x-2 (d) f(x)- ^*4/3 (a) y- f(x) -18x 4. Graph a function f(x) that gives rise to the derivative function f'(x) 0. Then graph a function 9(x) characterized by g(xo)0
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
3. (5 pts) For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter three, use the limit definition, Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than f and r. For...
3. Find the derivative of the following functions: (6 points) (a) x2y2- 10 = xey - 10x (b) x*(x+y) y3 (3x - y) (c) yex ycos(x2) dx 17 A is leaning aoainst a wall and sliding towards the floo
3. Find the derivative of the following functions: (6 points) (a) x2y2- 10 = xey - 10x (b) x*(x+y) y3 (3x - y) (c) yex ycos(x2) dx 17 A is leaning aoainst a wall and sliding towards the floo
1. The function f has derivative f' where f' is increasing and twice differentiable. Selected values of f' are given in the table above. It is known that f(0) = 3. (a) For f'(x), the conditions of the Mean Value Theorem are met on the closed interval (0,3). The conclusion of the Mean Value Theorem over the interval (0,3) for f'(x) is satisfied at c = 1. Find f"(c). (b) Use a right Riemann sum with the three subintervals indicated...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
(1 point) Functions of the form f(x)= x, where n= 1,2, 3.., are often called power functions (a) Use the limit definition of the derivative to find f'() for f(x)x. fx) (b) Use the limit definition of the derivative to find f '(x) for f(x) = f'(x) (c) Use the limit definition of the derivative to find f'(x) for f(x) = x.(Hint : (a + b) +4ab +b. Apply this rule to (x + h a +4ab+6a b within the...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
question - 4 plzzzzzzzzzzz draw the
graph
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Find the derivative of each of the following unctions: (e) w- 4u/2 (f) w=4u1/4 12 (c) y7x (b) y 63 2, Find the following: 0 (b) -9x1/3 (-oub du 3. Find f(1) and f(2) from the following functions: (C) f(x)--5x-2 (d) f(x)- ^*4/3 (a) y- f(x) -18x 4. Graph a function f(x) that gives rise to the derivative function f'(x) 0. Then graph a function 9(x) characterized by g(xo)0
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