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docker41 [41]
3 years ago
8

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

Mathematics
1 answer:
ankoles [38]3 years ago
5 0

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}

---------------------------------------------------

   (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}

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