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

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

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

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

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derivative of

y = 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}

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