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xnlghtmarexgo

Answered question

2021-12-07

Find the derivative of the following functions by first expanding the expression.

g (r) = (5 r^{3} + 3 r + 1) (r^{2} + 3)

Answer & Explanation

Symbee

Beginner2021-12-08Added 17 answers

Step 1
Given:

g (r) = (5 r^{3} + 3 r + 1) (r^{2} + 3)

g(r) can be expanded as,

g (r) = (5 r^{3} + 3 r + 1) (r^{2} + 3)

= 5 r^{5} + 15 r^{3} + 3 r^{3} + 9 r + r^{2} + 3

= 5 r^{5} + 18 r^{3} + r^{2} + 9 r + 3

Differentiating h(x) with respect to x,

g^{'} (r) = \frac{d}{d r} (5 r^{5} + 18 r^{3} + r^{2} + 9 r + 3)

= 25 r^{4} + 54 r^{2} + 2 r + 9

Hence,

g^{1} (r) = 25 r^{4} + 54 r^{2} + 2 r + 9

.
Step 3
Differentiating g(r) with respect to r,

g^{'} (r) = \frac{d}{d r} (23 r^{3} + r^{2} + 9 r + 3)

= 69 r^{2} + 2 r + 9

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