Question: "Find the derivative of the function. y=tan−1−6⋅x3"

Daniaal Sanchez

Answered question

2021-09-23

Find the derivative of the function.

y = \tan^{- 1} - 6 \cdot x^{3}

FieniChoonin

Skilled2021-09-24Added 102 answers

Step 1
We have to find the derivative of the function:

y = \tan^{- 1} (- 6 \cdot x^{3})

We know the formula of derivatives,

\frac{{d x}^{n}}{d x} = n x^{n - 1}

\frac{d \tan^{- 1} x}{d x} = \frac{1}{1 + x^{2}}

\frac{d \tan^{- 1} f (x)}{d x} = \frac{1}{1 + {(f (x))}^{2}} \frac{d f (x)}{d x}

Step 2
Differentiating the given function with respect to 'x' by applying above formula, we get

\frac{d y}{d x} = \frac{d \tan^{- 1} (- 6 \cdot x^{3})}{d x}

y^{'} = \frac{1}{1 + {(- 6 x^{3})}^{2}} \frac{d (- 6 x^{3})}{d x}

= \frac{1}{1 + 36 x^{6}} (- 6 \frac{{d x}^{3}}{d x})

= \frac{1}{1 + 36 x^{6}} (- 6 \times 3 x^{3 - 1})

= \frac{1}{1 + 36 x^{6}} (- 18 x^{2})

= - \frac{18 x^{2}}{1 + 36 x^{6}}

Hence,

y^{'} = - \frac{18 x^{2}}{1 + 36 x^{6}}

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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