What is the derivative of sqrt((sin(20x)^3)) ?

The derivative of sqrt((sin(20x)^3)) is 30cos(20x)sqrt(sin(20x))

What is the first derivative of sqrt((sin(20x)^3)) ?

The first derivative of sqrt((sin(20x)^3)) is 30cos(20x)sqrt(sin(20x))

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\frac{d}{d x} ((sin (20 x))^{3})

30 cos (20 x) sin (20 x)

Solution steps

\frac{d}{d x} ((sin (20 x))^{3})

Apply the chain rule:

\frac{1}{2 ( sin ( 20 x ) ) ^{3}} \frac{d}{d x} ((sin (20 x))^{3})

= \frac{1}{2 ( sin ( 20 x ) ) ^{3}} \frac{d}{d x} ((sin (20 x))^{3})

\frac{d}{d x} ((sin (20 x))^{3}) = 60 sin^{2} (20 x) cos (20 x)

= \frac{1}{2 ( sin ( 20 x ) ) ^{3}} \cdot 60 sin^{2} (20 x) cos (20 x)

Simplify

\frac{1}{2 sin ^{3} ( 20 x )} \cdot 60 sin^{2} (20 x) cos (20 x) : 30 cos (20 x) sin (20 x)

= 30 cos (20 x) sin (20 x)

What is the derivative of sqrt((sin(20x)^3)) ?
The derivative of sqrt((sin(20x)^3)) is 30cos(20x)sqrt(sin(20x))
What is the first derivative of sqrt((sin(20x)^3)) ?
The first derivative of sqrt((sin(20x)^3)) is 30cos(20x)sqrt(sin(20x))