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

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

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

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

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derivative of

f (x) = 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}

\frac{d}{d x} (\frac{( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 )})

y = 2 (6 x^{2} - 42 x + 49)

f (x) = 25 x

\int_{1}^{e} 3 x^{2} ln (x) d x

f (x) = 3 x^{\frac{1}{2}}

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