What is the derivative of f(x)=2sin^5(sqrt(x)) ?

The derivative of f(x)=2sin^5(sqrt(x)) is (5sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of f(x)=2sin^5(sqrt(x)) ?

The first derivative of f(x)=2sin^5(sqrt(x)) is (5sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

f (x) = 2 sin^{5} (x)

\frac{5 sin ^{4} ( x ) cos ( x )}{x}

Solution steps

\frac{d}{d x} (2 sin^{5} (x))

Take the constant out:

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

= 2 \frac{d}{d x} (sin^{5} (x))

Apply the chain rule:

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

= 5 (sin (x))^{4} \frac{d}{d x} (sin (x))

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

= 2 \cdot 5 (sin (x))^{4} \frac{cos ( x )}{2 x}

Simplify

2 \cdot 5 sin^{4} (x) \frac{cos ( x )}{2 x} : \frac{5 sin ^{4} ( x ) cos ( x )}{x}

= \frac{5 sin ^{4} ( x ) cos ( x )}{x}

x sin (x^{2})

y^{^{''}} - 4 y^{^{'}} + 3 y = - e^{- s}, y (0) = 0, y^{^{'}} (0) = 0

arcsec (2 x + 2)

\int 8 sin^{4} (x) cos^{2} (x) d x

\int e^{(2 x + 1)} d x

What is the derivative of f(x)=2sin^5(sqrt(x)) ?
The derivative of f(x)=2sin^5(sqrt(x)) is (5sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of f(x)=2sin^5(sqrt(x)) ?
The first derivative of f(x)=2sin^5(sqrt(x)) is (5sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))