What is the derivative of sin((pix)^9) ?

The derivative of sin((pix)^9) is cos(pi^9x^9)*9pi^9x^8

What is the first derivative of sin((pix)^9) ?

The first derivative of sin((pix)^9) is cos(pi^9x^9)*9pi^9x^8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

sin ((π x)^{9})

cos (π^{9} x^{9}) \cdot 9 π^{9} x^{8}

Solution steps

\frac{d}{d x} (sin ((π x)^{9}))

Simplify

sin ((π x)^{9}) : sin (π^{9} x^{9})

= \frac{d}{d x} (sin (π^{9} x^{9}))

Apply the chain rule:

cos (π^{9} x^{9}) \frac{d}{d x} (π^{9} x^{9})

= cos (π^{9} x^{9}) \frac{d}{d x} (π^{9} x^{9})

\frac{d}{d x} (π^{9} x^{9}) = 9 π^{9} x^{8}

= cos (π^{9} x^{9}) \cdot 9 π^{9} x^{8}

What is the derivative of sin((pix)^9) ?
The derivative of sin((pix)^9) is cos(pi^9x^9)*9pi^9x^8
What is the first derivative of sin((pix)^9) ?
The first derivative of sin((pix)^9) is cos(pi^9x^9)*9pi^9x^8