What is the derivative of-sin(pixpi) ?

The derivative of-sin(pixpi) is -pi^2cos(pix)

What is the first derivative of-sin(pixpi) ?

The first derivative of-sin(pixpi) is -pi^2cos(pix)

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\frac{d}{d x} (- sin (π x) π)

- π^{2} cos (π x)

Solution steps

\frac{d}{d x} (- sin (π x) π)

Take the constant out:

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

= - π \frac{d}{d x} (sin (π x))

Apply the chain rule:

cos (π x) \frac{d}{d x} (π x)

= cos (π x) \frac{d}{d x} (π x)

\frac{d}{d x} (π x) = π

= - π cos (π x) π

Simplify

- π cos (π x) π : - π^{2} cos (π x)

= - π^{2} cos (π x)

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