3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives...
Question 2. (20 points, 4 each) Apply the basic differentiation rules to find the derivatives of the functions given below. (a) f(x)=In(5x2+3x) - 2Vx3 (b) f(x)=(x2-3) (e3x-1 +2x) (c) 2x4+7xy+5x3=120 (d) S¢ + x)dx (e) S(x2 + e2x)dx
Find the indicated integral. Check your answers by differentiation. 1) du The slope f '(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find S (x). 2) f'(x) = 9x2 - 8x + 2; (0,7) 2) A) f(x) - 3x3 - 4x2 + 2x - 7 B) Ax) = 3x - 8 C)/(x) - 9x3 - 8x2 + 2x + 7...
Show your work and CIRCLE or BOX your final answer. No credit if work is not shown. Differentiate. 1) f(x) - 3x2 - 5x + 7 Basic Derivative Rules 1. (c)' = 0 2. Fix) + (x)] = f'(x) g'(x) 3. ) - 9(x)]* = f'() - g'(x) 4. Icf(x)]* = f'(x) 5. txx)-f(xlg'(x) + g(xY'x) f'(x)-f(x)g'(x) [g(x)] Derivatives of Trigonometric Functions sin(x) = cos(x) csc(x)=-csc(x)cot(x) * cos(x) = -sin(x) “sec(x) = sec(x) tan(x) tan(x) = sec (x) cot(x) =...
Use the rules to find the derivative f (x) = -3x e^x^5 + 2cos(2x^2 )
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
1a. Find the equation y-f(x)-f'(x.)*(x-%) of a tangent line to the graph of a polynomial function f(x) -2xN4-x+3 3x^*2 at the point x, -1. (See the files Derivatives.doc and Derivatives of a power function.doc) N-16 1 b. Find the equation y-f(xi)-f'(x.)*(x-%) tangent line to the graph of a function of a f(x)-4x atx, 2. (Use the chain rule of differentiation for finding f'(x,).)
derivatives order 0 Find higher the 2 la f(x) 3x + 72 tl Find f'(x) b f(x) = x, (4) f (x) find f"(x) = 205"- 2 find f(5 (x) 20
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x – 1)+8x²(2x – 1)+ 16x(x? + 1) and third derivative is f"(x) = 24x(2x – 1) +24(x + 1) +48x2. True False dy Given the equation x3 + 3 xy + y2 = 4. We find dx 2 x' + y by implicit differentiation and is to be y' = x + y2 True False Let f(x)= x...
#35,37
In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
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Let f(x) = x2 + 3x + 5. a) Find all derivatives of f(x). b) Find the value of f(n) (2) for all derivatives. c). Find the Taylor's series for f(x) centered at c = 2.