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

The derivative of sin^5(x^3) is 15x^2sin^4(x^3)cos(x^3)

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

The first derivative of sin^5(x^3) is 15x^2sin^4(x^3)cos(x^3)

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derivative of

sin^{5} (x^{3})

15 x^{2} sin^{4} (x^{3}) cos (x^{3})

Solution steps

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

Apply the chain rule:

5 (sin (x^{3}))^{4} \frac{d}{d x} (sin (x^{3}))

= 5 (sin (x^{3}))^{4} \frac{d}{d x} (sin (x^{3}))

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

= 5 (sin (x^{3}))^{4} cos (x^{3}) \cdot 3 x^{2}

Simplify

= 15 x^{2} sin^{4} (x^{3}) cos (x^{3})

What is the derivative of sin^5(x^3) ?
The derivative of sin^5(x^3) is 15x^2sin^4(x^3)cos(x^3)
What is the first derivative of sin^5(x^3) ?
The first derivative of sin^5(x^3) is 15x^2sin^4(x^3)cos(x^3)