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

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

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

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

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

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

Solution steps

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

\int_{1}^{5} \frac{x - 1}{x ^{3} + x} d x

9 y^{^{'}} + y = 5 t^{2}

n = 1 \sum \infty (- \frac{3}{5})^{n}

\frac{d}{d u} (tan (\frac{u}{v}))

\frac{d x}{d y} = y

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