What is the derivative of f(x)=8sin^4(sqrt(x)) ?

The derivative of f(x)=8sin^4(sqrt(x)) is (16sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of f(x)=8sin^4(sqrt(x)) ?

The first derivative of f(x)=8sin^4(sqrt(x)) is (16sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

f (x) = 8 sin^{4} (x)

\frac{16 sin ^{3} ( x ) cos ( x )}{x}

Solution steps

\frac{d}{d x} (8 sin^{4} (x))

Take the constant out:

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

= 8 \frac{d}{d x} (sin^{4} (x))

Apply the chain rule:

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

= 4 (sin (x))^{3} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 x}

= 8 \cdot 4 (sin (x))^{3} \frac{cos ( x )}{2 x}

Simplify

8 \cdot 4 sin^{3} (x) \frac{cos ( x )}{2 x} : \frac{16 sin ^{3} ( x ) cos ( x )}{x}

= \frac{16 sin ^{3} ( x ) cos ( x )}{x}

\frac{d}{d x} (6 x^{5} - 15 x^{4} + 10 x^{3})

\frac{\partial}{\partial x} (\frac{x}{y + 5 z})

\frac{d}{d x} (3^{5 x + 2})

(- 3 x + 28)^{\frac{5}{4}}

\int_{0}^{7} \frac{1}{49 + x ^{2}} d x

What is the derivative of f(x)=8sin^4(sqrt(x)) ?
The derivative of f(x)=8sin^4(sqrt(x)) is (16sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of f(x)=8sin^4(sqrt(x)) ?
The first derivative of f(x)=8sin^4(sqrt(x)) is (16sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))