What is the derivative of 8sin^3(sqrt(x)) ?

The derivative of 8sin^3(sqrt(x)) is (12sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of 8sin^3(sqrt(x)) ?

The first derivative of 8sin^3(sqrt(x)) is (12sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

8 sin^{3} (x)

\frac{12 sin ^{2} ( x ) cos ( x )}{x}

Solution steps

\frac{d}{d x} (8 sin^{3} (x))

Take the constant out:

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

= 8 \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)) = \frac{cos ( x )}{2 x}

= 8 \cdot 3 (sin (x))^{2} \frac{cos ( x )}{2 x}

Simplify

8 \cdot 3 sin^{2} (x) \frac{cos ( x )}{2 x} : \frac{12 sin ^{2} ( x ) cos ( x )}{x}

= \frac{12 sin ^{2} ( x ) cos ( x )}{x}

\int_{0}^{π} (sec^{2} (\frac{x}{3})) d x

\frac{d}{d x} (e^{x s e c (x)})

\frac{d}{d x} (2 cos (x^{2}) - 4 x^{2} sin (x^{2}))

f (x) = (x^{2} + x) (6 - x)

x \to 4 + lim (3 x - 5)

What is the derivative of 8sin^3(sqrt(x)) ?
The derivative of 8sin^3(sqrt(x)) is (12sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of 8sin^3(sqrt(x)) ?
The first derivative of 8sin^3(sqrt(x)) is (12sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))