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abreviatsjw

Answered question

2021-12-10

Find the derivatives of the following functions using chain rule.

f (x) = {(4 x^{2} - 5 x)}^{3}

Answer & Explanation

Medicim6

Beginner2021-12-11Added 33 answers

Step 1
Find derivative using chain rule

y = {(4 x^{2} - 5 x)}^{3}

Step 2
Concept: If

y = {(f (x))}^{n}

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

y = {(4 x^{2} - 5 x)}^{3}

\frac{d y}{d x} = 3 {(4 x^{2} - 5 x)}^{2} \frac{d}{d x} (4 x^{2} - 5 x)

= 3 {(4 x^{2} - 5 x)}^{2} (8 x - 5)

\frac{d y}{d x} = 3 (8 x - 5) {(4 x^{2} - 5 x)}^{2}

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