Get the solution to "Find the derivatives of the functions y=x−2sin⁡2(x3)"

Trent Carpenter

Answered question

2021-05-23

Find the derivatives of the functions

y = x - 2 \sin 2 (x^{3})

svartmaleJ

Skilled2021-05-24Added 92 answers

Step 1
We have to find derivatives of the functions:

y = x - 2 \sin 2 (x^{3})

We know formula of differentiation,

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

\frac{d \sin f (x)}{d x} = \cos f (x) \frac{d f (x)}{d x}

So applying above rule and differentiating the function with respect to x, we get

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

Step 2
Simplifying further,

\frac{d y}{d x} = 1 - 2 (\cos 2 (x^{3})) \frac{d 2 x^{3}}{d x}

= 1 - 2 (\cos 2 (x^{3})) (2 \times 3 x^{3 - 1})

= 1 - 12 x^{2} \cos 2 (x^{3})

Hence, derivative of the function is

= 1 - 12 x^{2} \cos 2 (x^{3})

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