Question

Use the chain rule to find the derivative of each of the following :

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

$\frac{dy}{dx}$ = f'(g(x)) × g'(x)

(a)

y = $\frac{2}{(3x^2-x+7)^3}$ = 2 ($3x^2-x+7)^{-3}$

$\frac{dy}{dx}$ = 2. - 3 $(3x^2-x+7)^{-4}$ × $\frac{d}{dx}$ (3x² - x + 7)

   = - 6 $(3x^2-x+7)^{-4}$ × (6x - 1)

   = $\frac{-6(6x-1)}{(3x^2-x+7)^4}$

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   (b)

y = $(4x-10)^{10}$

$\frac{dy}{dx}$ = 10$(4x-10)^{9}$ × $\frac{d}{dx}$(4x - 10)

    = 10$(4x-10)^{9}$ × 4

     = 40$(4x-10)^{9}$