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

The derivative of f(x)=2(sin^3(x)) is 6sin^2(x)cos(x)

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

The first derivative of f(x)=2(sin^3(x)) is 6sin^2(x)cos(x)

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derivative of

f (x) = 2 (sin^{3} (x))

6 sin^{2} (x) cos (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Simplify

= 6 sin^{2} (x) cos (x)

\int \frac{sin ( 2 x )}{14 + cos ^{2} ( x )} d x

y^{^{'}} + \frac{2}{x} y = y^{2}, y (1) = 3

\frac{d}{d x} (\frac{a}{2 y})

t^{3} y^{^{'}} + 4 t^{2} y = 0

\int \frac{3 sin ^{3} ( x )}{cos ( x )} d x

What is the derivative of f(x)=2(sin^3(x)) ?
The derivative of f(x)=2(sin^3(x)) is 6sin^2(x)cos(x)
What is the first derivative of f(x)=2(sin^3(x)) ?
The first derivative of f(x)=2(sin^3(x)) is 6sin^2(x)cos(x)