What is the derivative of 2sin^2(pix) ?

The derivative of 2sin^2(pix) is 4pisin(pix)cos(pix)

What is the first derivative of 2sin^2(pix) ?

The first derivative of 2sin^2(pix) is 4pisin(pix)cos(pix)

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\frac{d}{d x} (2 sin^{2} (π x))

4 π sin (π x) cos (π x)

Solution steps

\frac{d}{d x} (2 sin^{2} (π x))

Take the constant out:

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

= 2 \frac{d}{d x} (sin^{2} (π x))

Apply the chain rule:

2 sin (π x) \frac{d}{d x} (sin (π x))

= 2 sin (π x) \frac{d}{d x} (sin (π x))

\frac{d}{d x} (sin (π x)) = cos (π x) π

= 2 \cdot 2 sin (π x) cos (π x) π

Simplify

= 4 π sin (π x) cos (π x)

\frac{\partial}{\partial x} (ln (x - 3 y))

\frac{d}{d x} (1 + cos (3 π x))

\int \frac{1}{1 + cos ( u )} d u

\int ln (1 + y^{2}) d y

\int \frac{2}{x + 5} d x

What is the derivative of 2sin^2(pix) ?
The derivative of 2sin^2(pix) is 4pisin(pix)cos(pix)
What is the first derivative of 2sin^2(pix) ?
The first derivative of 2sin^2(pix) is 4pisin(pix)cos(pix)