Use the chain rule to find the derivative of each of the following : a. \frac{2}{(3x^2-x+7)^3} b. [tex](4x-10)^

Question

Use the chain rule to find the derivative of each of the following :
a. \frac{2}{(3x^2-x+7)^3}

b. (4x-10)^1^0

in progress 0
Huyền Thanh 3 years 2021-07-31T05:08:16+00:00 1 Answers 11 views 0

Answers ( )

  1. niczorrrr
    0
    2021-07-31T05:10:01+00:00
    Reply

    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}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )