What is the derivative of 5picos(pix) ?

The derivative of 5picos(pix) is -5pi^2sin(pix)

What is the first derivative of 5picos(pix) ?

The first derivative of 5picos(pix) is -5pi^2sin(pix)

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\frac{d}{d x} (5 π cos (π x))

- 5 π^{2} sin (π x)

Solution steps

\frac{d}{d x} (5 π cos (π x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 π \frac{d}{d x} (cos (π x))

Apply the chain rule:

- sin (π x) \frac{d}{d x} (π x)

= - sin (π x) \frac{d}{d x} (π x)

\frac{d}{d x} (π x) = π

= 5 π (- sin (π x) π)

Simplify

5 π (- sin (π x) π) : - 5 π^{2} sin (π x)

= - 5 π^{2} sin (π x)

What is the derivative of 5picos(pix) ?
The derivative of 5picos(pix) is -5pi^2sin(pix)
What is the first derivative of 5picos(pix) ?
The first derivative of 5picos(pix) is -5pi^2sin(pix)