What is the derivative of cos((pix^8)) ?

The derivative of cos((pix^8)) is -sin(pi^8x^8)*8pi^8x^7

What is the first derivative of cos((pix^8)) ?

The first derivative of cos((pix^8)) is -sin(pi^8x^8)*8pi^8x^7

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\frac{d}{d x} (cos ((π x)^{8}))

- sin (π^{8} x^{8}) \cdot 8 π^{8} x^{7}

Solution steps

\frac{d}{d x} (cos ((π x)^{8}))

Simplify

cos ((π x)^{8}) : cos (π^{8} x^{8})

= \frac{d}{d x} (cos (π^{8} x^{8}))

Apply the chain rule:

- sin (π^{8} x^{8}) \frac{d}{d x} (π^{8} x^{8})

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

\frac{d}{d x} (π^{8} x^{8}) = 8 π^{8} x^{7}

= - sin (π^{8} x^{8}) \cdot 8 π^{8} x^{7}

\int 8 sin^{6} (x) cos (x) d x

y = arctan (cos (x))

\frac{d}{d x} (e^{2 x} + x^{3})

\frac{\partial}{\partial y} (2 x^{3} y + cos (x^{2}))

\frac{d}{d x} (C e^{3 x})

What is the derivative of cos((pix^8)) ?
The derivative of cos((pix^8)) is -sin(pi^8x^8)*8pi^8x^7
What is the first derivative of cos((pix^8)) ?
The first derivative of cos((pix^8)) is -sin(pi^8x^8)*8pi^8x^7