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danrussekme

Answered question

2021-12-06

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

f (x) = (2 x + 1) (3 x^{2} + 2)

Answer & Explanation

Lible1953

Beginner2021-12-07Added 16 answers

Step 1
Given:

f (x) = (2 x + 1) (3 x^{2} + 2)

f(x) can be expanded as,

f (x) = (2 x + 1) (3 x^{2} + 2)

= 6 x^{3} + 4 x + 3 x^{2} + 2

= 6 x^{3} + 3 x^{2} + 4 x + 2

Step 2
Differentiating f(x) with respect to x,

f^{'} (x) = \frac{d}{d x} (6 x^{3} + 3 x^{2} + 4 x + 2)

= 18 x^{2} + 6 x + 4

Hence,

f^{'} (x) = 18 x^{2} + 6 x + 4

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