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Popular >

derivative of sin((pix)^9)

Solution

derivative of

sin ((π x)^{9})

Solution

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}

Popular Examples

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[x^{2} (x^{2} + 5 x)]^{6}

extreme f(x)=y^2-xy extreme points

f (x) = y^{2} - x y

integral of x^2(x-2)

\int x^{2} (x - 2) d x

sum from n=0 to infinity of (n!)/(103^n)

n = 0 \sum \infty \frac{n !}{10 3 ^{n}}

(\partial)/(\partial y)(x^2+2xy^2+2y^2)

\frac{\partial}{\partial y} (x^{2} + 2 x y^{2} + 2 y^{2})

Frequently Asked Questions (FAQ)

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