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

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

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

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

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derivative of

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

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

Solution steps

\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}

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

Simplify

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

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

4 + x

\int \frac{1}{( x ^{2} - x - 2 ) ( x - 2 )} d x

y^{^{'}} = 2 y - y^{2}

\int 2 p x d x

\frac{d}{d x} ((cos (2 x))^{x})

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