What is the derivative of sin^2(5x) ?

The derivative of sin^2(5x) is 5sin(10x)

What is the first derivative of sin^2(5x) ?

The first derivative of sin^2(5x) is 5sin(10x)

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derivative of

sin^{2} (5 x)

5 sin (10 x)

Solution steps

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

Apply the chain rule:

2 sin (5 x) \frac{d}{d x} (sin (5 x))

= 2 sin (5 x) \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 2 sin (5 x) cos (5 x) \cdot 5

Simplify

2 sin (5 x) cos (5 x) \cdot 5 : 5 sin (10 x)

= 5 sin (10 x)

What is the derivative of sin^2(5x) ?
The derivative of sin^2(5x) is 5sin(10x)
What is the first derivative of sin^2(5x) ?
The first derivative of sin^2(5x) is 5sin(10x)