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

The derivative of sin^2(ax) is asin(2ax)

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

The first derivative of sin^2(ax) is asin(2ax)

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\frac{d}{d x} (sin^{2} (a x))

a sin (2 a x)

Solution steps

\frac{d}{d x} (sin^{2} (a x))

Apply the chain rule:

2 sin (a x) \frac{d}{d x} (sin (a x))

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

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

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

Use the Double Angle identity:

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

= a sin (2 a x)

\frac{d}{d x} (\frac{x ^{2}}{5 + 2 x})

\int \frac{x}{3 x ^{2} + 5} d x

\frac{d}{d x} (\frac{4}{( x + 2 ) ^{2} + 16})

\frac{\partial}{\partial x} ((e^{x} - x) cos (y))

\frac{d}{d t} (- 32 t)

What is the derivative of sin^2(ax) ?
The derivative of sin^2(ax) is asin(2ax)
What is the first derivative of sin^2(ax) ?
The first derivative of sin^2(ax) is asin(2ax)