Find out the answer to "Chain Rule and Higher Order Derivatives. Find the..."

hexacordoK

Answered question

2021-04-23

Chain Rule and Higher Order Derivatives. Find the derivative

f (x) = {(5 x^{2} - 2 x + 1)}^{3}

Answer & Explanation

Adnaan Franks

Skilled2021-04-25Added 92 answers

Step 1
the given function is:
$f (x) = {(5 x^{2} - 2 x + 1)}^{3}$
we have to find the derivative of the given function.
Step 2
$f (x) = {(5 x^{2} - 2 x + 1)}^{3}$
differentiating both the sides with respect to 'x' we get
$\frac{d}{d x} f (x) = \frac{d}{d x} {(5 x^{2} - 2 x + 1)}^{3}$
$f^{'} (x) = 3 {(5 x^{2} - 2 x + 1)}^{2} \times \frac{d}{d x} (5 x^{2} - 2 x + 1)$
$= 3 {(5 x^{2} - 2 x + 1)}^{2} (5 \frac{d}{d x} (x^{2}) - 2 \frac{d (x)}{d x} + \frac{d}{d x} (1))$
$= 3 {(5 x^{2} - 2 x + 1)}^{2} (5 (2 x) - 2 (1) + 0))$
$= 3 {(5 x^{2} - 2 x + 1)}^{2} (10 x - 2)$
therefore the derivative of the given function $f (x) = {(5 x^{2} - 2 x + 1)}^{3} i s 3 {(5 x^{2} - 2 x + 1)}^{2} (10 x - 2)$

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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