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

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

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

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

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\frac{d}{d x} (sin^{2} (π x))

π sin (2 π x)

Solution steps

\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 sin (π x) cos (π x) π

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= π sin (2 π x)

\frac{d y}{d x} = \frac{2 sec ( y )}{( x - 2 ) ^{2}}

\frac{\partial}{\partial y} (x e^{2 y + 3 z})

\int e^{- ia x} d x

\int 17 tan^{3} (θ) d θ

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