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nicekikah

Answered question

2021-10-15

Derivatives Find and simplify the derivative of the following functions

h (x) = (5 x^{7} + 5 x) (6 x^{3} + 3 x^{2} + 3)

Brighton

Skilled2021-10-16Added 103 answers

Step 1
Given,

h (x) = (5 x^{7} + 5 x) (6 x^{3} + 3 x^{2} + 3)

Step 2
Concept used:

\frac{d}{d x} (f (x) g (x)) = g (x) \frac{d}{d x} (f (x)) + f (x) \frac{d}{d x} (g (x))

\frac{d}{d x} (x^{n}) = n x^{n - 1}

\frac{d}{d x} (c) = 0

Step 3
On differentiating with respect to x, to obtain

\frac{d}{d x} (h (x)) = \frac{d}{d x} [(5 x^{7} + 5 x) (6 x^{3} + 3 x^{2} + 3)]

h^{'} (x) = (6 x^{3} + 3 x^{2} + 3) \frac{d}{d x} (5 x^{7} + 5 x) + (5 x^{7} + 5 x) \frac{d}{d x} (6 x^{3} + 3 x^{2} + 3)

h^{'} (x) = (6 x^{3} + 3 x^{2} + 3) (35 x^{6} + 5) + (5 x^{7} + 5 x) (18 x^{2} + 6 x + 0)

h^{'} (x) = 210 x^{9} + 30 x^{3} + 105 x^{8} + 15 x^{2} + 105 x^{6} + 15 + 90 x^{9} + 30 x^{8} + 90 x^{3} + 30 x^{2}

h^{'} (x) = 300 x^{9} + 135 x^{8} + 105 x^{6} + 120 x^{3} + 45 x^{2} + 15

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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