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Popular Calculus >

derivative of cos((pix)^3)

Solution

derivative of

cos ((π x)^{3})

Solution

- sin (π^{3} x^{3}) \cdot 3 π^{3} x^{2}

Solution steps

\frac{d}{d x} (cos ((π x)^{3}))

Simplify

cos ((π x)^{3}) : cos (π^{3} x^{3})

= \frac{d}{d x} (cos (π^{3} x^{3}))

Apply the chain rule:

- sin (π^{3} x^{3}) \frac{d}{d x} (π^{3} x^{3})

= - sin (π^{3} x^{3}) \frac{d}{d x} (π^{3} x^{3})

\frac{d}{d x} (π^{3} x^{3}) = 3 π^{3} x^{2}

= - sin (π^{3} x^{3}) \cdot 3 π^{3} x^{2}

Graph

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\int_{0}^{\frac{1}{2}} 7 arccos (x) d x

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Frequently Asked Questions (FAQ)

What is the derivative of cos((pix)^3) ?
The derivative of cos((pix)^3) is -sin(pi^3x^3)*3pi^3x^2
What is the first derivative of cos((pix)^3) ?
The first derivative of cos((pix)^3) is -sin(pi^3x^3)*3pi^3x^2