(1 pt) If f(x) = x8 sin (x), the derivative of f with respect to X...
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...
Find a formula for terms of f (x) = sin x or g(x) = COS X Enter your answer in terms of sin (x) or uments of functions in parentheses. For example, sin
6. o 1 points Use logarithmic differentiation or an alternative method to find the derivative of the function y=x8 cos x Submit Answer Save Progress
6. o 1 points Use logarithmic differentiation or an alternative method to find the derivative of the function y=x8 cos x Submit Answer Save Progress
9 - sin (1 point) Find the derivative of f(x) = 5 - COS f'(x) = Preview My Answers Submit Answers You have attempted this problem 0 times. You have 2 attempts remaining. Email WebWork TA
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina
2. Consider f(x)={ x2 sin (1) xメ0 x) = (a) Show the function has a derivative for xE [0,1 (b) Show the function does not have a second derivative for x E [0,1] (c) Does this violate our understanding of holomorphic functions?
6. Show F,{f"(x)}=-Ff()}+0f(0). F{f(x)} = f (x) sin ox dr and f"(x) is the second derivative of fx) with respect to x (5%), and write down the assumptions that f(x), f'(x) and f"(x) have to satisfy. (5%)
6. Show F,{f"(x)}=-Ff()}+0f(0). F{f(x)} = f (x) sin ox dr and f"(x) is the second derivative of fx) with respect to x (5%), and write down the assumptions that f(x), f'(x) and f"(x) have to satisfy. (5%)
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
2y (1 pt) Suppose f(z, y) sin (-) and u is the unit vector in the direction of 〈-1 , 0). Then, (a) ▽f(x, y)- ((-2y)/(хл2)cos(2y)/x),((2/x)cos(2y/x)) (b) ▽f(2, π) = (pi/4)(M2)
2y (1 pt) Suppose f(z, y) sin (-) and u is the unit vector in the direction of 〈-1 , 0). Then, (a) ▽f(x, y)- ((-2y)/(хл2)cos(2y)/x),((2/x)cos(2y/x)) (b) ▽f(2, π) = (pi/4)(M2)
Find the first derivative with respect to the domain variable for the following functions. 4. f(x) = (x - 2)(x² + 2x +4)