en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin^5(4x^5)

Solution

derivative of

sin^{5} (4 x^{5})

Solution

100 x^{4} sin^{4} (4 x^{5}) cos (4 x^{5})

Solution steps

\frac{d}{d x} (sin^{5} (4 x^{5}))

Apply the chain rule:

5 (sin (4 x^{5}))^{4} \frac{d}{d x} (sin (4 x^{5}))

= 5 (sin (4 x^{5}))^{4} \frac{d}{d x} (sin (4 x^{5}))

\frac{d}{d x} (sin (4 x^{5})) = cos (4 x^{5}) \cdot 20 x^{4}

= 5 (sin (4 x^{5}))^{4} cos (4 x^{5}) \cdot 20 x^{4}

Simplify

= 100 x^{4} sin^{4} (4 x^{5}) cos (4 x^{5})

Popular Examples

integral of sin(2x)(sin^2(x)+pi)^{3/2}

\int sin (2 x) (sin^{2} (x) + π)^{\frac{3}{2}} d x

derivative of f(x)=e^{sin(x)}derivative of

f (x) = e^{s i n (x)}

tangent of y=2x^3-8x,(-2,0)tangent of

y = 2 x^{3} - 8 x, (- 2, 0)

integral of e^{-t(s+1)}

\int e^{- t (s + 1)} d t

inverse oflaplace (e^{-s})/(1-s)inverse laplace

\frac{e ^{- s}}{1 - s}

Frequently Asked Questions (FAQ)

What is the derivative of sin^5(4x^5) ?
The derivative of sin^5(4x^5) is 100x^4sin^4(4x^5)cos(4x^5)
What is the first derivative of sin^5(4x^5) ?
The first derivative of sin^5(4x^5) is 100x^4sin^4(4x^5)cos(4x^5)