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)

\int x^{- 8} d x

y = \frac{x}{1 + x ^{2}}, at x = 0

\frac{d y}{d t} = 3 y - 1

e^{x} \cdot sin (x)

x \to 2 lim (- 16 x^{2} + 76 x)

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)