What is the derivative of cos((pix^7)) ?

The derivative of cos((pix^7)) is -sin(pi^7x^7)*7pi^7x^6

What is the first derivative of cos((pix^7)) ?

The first derivative of cos((pix^7)) is -sin(pi^7x^7)*7pi^7x^6

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\frac{d}{d x} (cos ((π x)^{7}))

- sin (π^{7} x^{7}) \cdot 7 π^{7} x^{6}

Solution steps

\frac{d}{d x} (cos ((π x)^{7}))

Simplify

cos ((π x)^{7}) : cos (π^{7} x^{7})

= \frac{d}{d x} (cos (π^{7} x^{7}))

Apply the chain rule:

- sin (π^{7} x^{7}) \frac{d}{d x} (π^{7} x^{7})

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

\frac{d}{d x} (π^{7} x^{7}) = 7 π^{7} x^{6}

= - sin (π^{7} x^{7}) \cdot 7 π^{7} x^{6}

What is the derivative of cos((pix^7)) ?
The derivative of cos((pix^7)) is -sin(pi^7x^7)*7pi^7x^6
What is the first derivative of cos((pix^7)) ?
The first derivative of cos((pix^7)) is -sin(pi^7x^7)*7pi^7x^6