What is the derivative of f(x)=2sin^4(sqrt(x)) ?

The derivative of f(x)=2sin^4(sqrt(x)) is (4sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of f(x)=2sin^4(sqrt(x)) ?

The first derivative of f(x)=2sin^4(sqrt(x)) is (4sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

f (x) = 2 sin^{4} (x)

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

Solution steps

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

Take the constant out:

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

= 2 \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}

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

Simplify

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

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

What is the derivative of f(x)=2sin^4(sqrt(x)) ?
The derivative of f(x)=2sin^4(sqrt(x)) is (4sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of f(x)=2sin^4(sqrt(x)) ?
The first derivative of f(x)=2sin^4(sqrt(x)) is (4sin^3(sqrt(x))cos(sqrt(x)))/(sqrt(x))