Question 2. (20 points, 4 each) Apply the basic differentiation rules to find the derivatives of...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
4) (5 points) Use the definition of the differentiation to find the derivative of f(x) x2 +3x.
4) (5 points) Use the definition of the differentiation to find the derivative of f(x) x2 +3x.
. Find the first derivatives (dy/dx) for each of the following functions. Do not need to simplify. (3 points each) A. y = (2x^5 + 3x^3)^2 B. y = (8x^3-56x^2+3x)/(x+12) C. y= (6x2 + 3x) (x – 4x3)
QUESTION 9 Apply the techniques of logarithmic differentiation to find the derivative of the given function f(x). [Hint: first take the logarithm of both sides and simplify using properties of logarithms. Then differentiate implicitly.) F) - ** (3x+1) {f(x) = {{x^2 (3x + 1)^3} /(sqrt(x^2 + 4))] } TTTT Paragi Arial 3 (12p *DOQ E T' T. . 15 25 Path: P QUESTION 10 Find the derivative of the following expression involving inverse trigonometric functions. g(x) = arctan x +...
(4 points) 8. Use partial derivatives to perform implicit differentiation to find dy if 5x® y2 + sin (z^y) = 2y4 + 3x, where y is a differentiable function of x.
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...
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
Anti-differentiation Question 1. Find the function f(x) if 1. f'(x) = 0.5e -0.2x, f(0) = 0 2. f'(x) = x2 + Vx, f(1) = 3 3. f'(x) = 1 7x Question 2. Find the number k: 14t - +0 e 4x-1 2.[(4 – x)"dx = kin/4 – xl + c 3.5(3x+2)*dx = k(3x + 2)5+C
please help me with these. Thanks.
4. Use implicit differentiation to find an equation of the tangent line to the graph y2 + In xy = 2 of at the point (e, 1) )(-5) using formula for the derivative of the inverse 5. Consider f(x) = x + 3x - 1. Find (f function. 6. Consider the following function and its inverse f(x) = x-4 f(x) = x2 +4, point (5,1) point (1,5) x20 a) Graph both functions on the...