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Popular >

derivative of f(x)=sqrt(sin^3(18x))

Solution

derivative of

f (x) = sin^{3} (18 x)

Solution

\frac{1}{2 sin ^{3} ( 18 x )} \cdot 54 sin^{2} (18 x) cos (18 x)

Solution steps

\frac{d}{d x} (sin^{3} (18 x))

Apply the chain rule:

\frac{1}{2 sin ^{3} ( 18 x )} \frac{d}{d x} (sin^{3} (18 x))

= \frac{1}{2 sin ^{3} ( 18 x )} \frac{d}{d x} (sin^{3} (18 x))

\frac{d}{d x} (sin^{3} (18 x)) = 54 sin^{2} (18 x) cos (18 x)

= \frac{1}{2 sin ^{3} ( 18 x )} \cdot 54 sin^{2} (18 x) cos (18 x)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(sin^3(18x)) ?
The derivative of f(x)=sqrt(sin^3(18x)) is 1/(2sqrt(sin^3(18x)))*54sin^2(18x)cos(18x)
What is the first derivative of f(x)=sqrt(sin^3(18x)) ?
The first derivative of f(x)=sqrt(sin^3(18x)) is 1/(2sqrt(sin^3(18x)))*54sin^2(18x)cos(18x)