Theorem: The Chain Rule provided If m(x) = EI(x) is a composite function, then that E'[I(x)) and I'(a) exist.

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

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Q: f(x) = (2x3 tan(x) – e-*)10 and g(x) = /(3x – 4)² – sin(x). %3D %3D

A: We have to use the chain rule to find the derivatives of f(x) and g(x)   We also have to find…

Q: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Let g(s) = (282)7. Then g'(s) is g'(2) is g" (s) is and g' (2) is "

A: Solving the following problem

Q: If g(x) = x' In(x), for x> 0, then determine g'(x

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Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: Differentiating the function f(x), using the Chain Rule. f(x) = {Vx5 + 6x f'(x) = =(x5 + 6x) 3 A 5x4…

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