Answered: "Find the following derivatives. x31−x2" - Plainmath

Reeves

Answered question

2021-10-21

Find the following derivatives.

x^{3} \sqrt{1 - x^{2}}

Answer & Explanation

Maciej Morrow

Skilled2021-10-22Added 98 answers

Step 1
The given function is:

f (x) = x^{3} \sqrt{1 - x^{2}}

Step 2
Now using product rule the derivative of the given function is:

\frac{d}{d x} (x^{3} \sqrt{1 - x^{2}}) = \sqrt{1 - x^{2}} \frac{d}{d x} (x^{3}) + x^{3} \frac{d}{d x} (\sqrt{1 - x^{2}})

= (\sqrt{1 - x^{2}}) (3 x^{2}) + x^{3} (\frac{- x}{\sqrt{1 - x^{2}}})

= 3 x^{2} \sqrt{1 - x^{2}} - \frac{x^{4}}{\sqrt{1 - x^{2}}}

= \frac{3 x^{2} - 3 x^{4} - x^{4}}{\sqrt{1 - x^{2}}}

\frac{d}{d x} (x^{3} \sqrt{1 - x^{2}}) = \frac{x^{2} (3 - 4 x^{2})}{\sqrt{1 - x^{2}}}

.

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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