What is the derivative of sin^3(5x^2) ?

The derivative of sin^3(5x^2) is 30xsin^2(5x^2)cos(5x^2)

What is the first derivative of sin^3(5x^2) ?

The first derivative of sin^3(5x^2) is 30xsin^2(5x^2)cos(5x^2)

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\frac{d}{d x} (sin^{3} (5 x^{2}))

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

Solution steps

\frac{d}{d x} (sin^{3} (5 x^{2}))

Apply the chain rule:

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

= 3 (sin (5 x^{2}))^{2} \frac{d}{d x} (sin (5 x^{2}))

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

= 3 (sin (5 x^{2}))^{2} cos (5 x^{2}) \cdot 10 x

Simplify

= 30 x sin^{2} (5 x^{2}) cos (5 x^{2})

\int \frac{1}{5 x ^{3}} d x

\int 4 x y e^{x y^{2}} d y

f (x) = x^{4} - 20 x^{2} + 64, at x = - 2

24 x^{3} + 24 x^{2}

\frac{d}{d x} (2 x^{2} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}})

What is the derivative of sin^3(5x^2) ?
The derivative of sin^3(5x^2) is 30xsin^2(5x^2)cos(5x^2)
What is the first derivative of sin^3(5x^2) ?
The first derivative of sin^3(5x^2) is 30xsin^2(5x^2)cos(5x^2)