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

The derivative of sin^2(5x^2) is 20xsin(5x^2)cos(5x^2)

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

The first derivative of sin^2(5x^2) is 20xsin(5x^2)cos(5x^2)

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

20 x sin (5 x^{2}) cos (5 x^{2})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (5 x^{2})) = cos (5 x^{2}) \cdot 10 x

= 2 sin (5 x^{2}) cos (5 x^{2}) \cdot 10 x

Simplify

= 20 x sin (5 x^{2}) cos (5 x^{2})

What is the derivative of sin^2(5x^2) ?
The derivative of sin^2(5x^2) is 20xsin(5x^2)cos(5x^2)
What is the first derivative of sin^2(5x^2) ?
The first derivative of sin^2(5x^2) is 20xsin(5x^2)cos(5x^2)