What is the derivative of y=sin((pix)^4) ?

The derivative of y=sin((pix)^4) is cos(pi^4x^4)*4pi^4x^3

What is the first derivative of y=sin((pix)^4) ?

The first derivative of y=sin((pix)^4) is cos(pi^4x^4)*4pi^4x^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = sin ((π x)^{4})

cos (π^{4} x^{4}) \cdot 4 π^{4} x^{3}

Solution steps

\frac{d}{d x} (sin ((π x)^{4}))

Simplify

sin ((π x)^{4}) : sin (π^{4} x^{4})

= \frac{d}{d x} (sin (π^{4} x^{4}))

Apply the chain rule:

cos (π^{4} x^{4}) \frac{d}{d x} (π^{4} x^{4})

= cos (π^{4} x^{4}) \frac{d}{d x} (π^{4} x^{4})

\frac{d}{d x} (π^{4} x^{4}) = 4 π^{4} x^{3}

= cos (π^{4} x^{4}) \cdot 4 π^{4} x^{3}

What is the derivative of y=sin((pix)^4) ?
The derivative of y=sin((pix)^4) is cos(pi^4x^4)*4pi^4x^3
What is the first derivative of y=sin((pix)^4) ?
The first derivative of y=sin((pix)^4) is cos(pi^4x^4)*4pi^4x^3