en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(sin(2x^3-1))^2

Solution

derivative of

y = (sin (2 x^{3} - 1))^{2}

Solution

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

Solution steps

\frac{d}{d x} ((sin (2 x^{3} - 1))^{2})

Apply the chain rule:

2 sin (2 x^{3} - 1) \frac{d}{d x} (sin (2 x^{3} - 1))

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

\frac{d}{d x} (sin (2 x^{3} - 1)) = cos (2 x^{3} - 1) \cdot 6 x^{2}

= 2 sin (2 x^{3} - 1) cos (2 x^{3} - 1) \cdot 6 x^{2}

Simplify

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

Popular Examples

integral from 1 to 3 of 19r^3ln(r)

\int_{1}^{3} 19 r^{3} ln (r) d r

y^{''}+5y^'+4y=te^{-t}

y^{^{''}} + 5 y^{^{'}} + 4 y = t e^{- t}

integral of (x^3-3x+2)/((x+1)(x-1)^3)

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

integral of ((2x)/(e^x))

\int (\frac{2 x}{e ^{x}}) d x

integral from 0 to pi/2 of sin(2x-pi)

\int_{0}^{\frac{π}{2}} sin (2 x - π) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(sin(2x^3-1))^2 ?
The derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)
What is the first derivative of y=(sin(2x^3-1))^2 ?
The first derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)