What is the derivative of f(x)=4sin^5(sqrt(x)) ?

The derivative of f(x)=4sin^5(sqrt(x)) is (10sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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

The first derivative of f(x)=4sin^5(sqrt(x)) is (10sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

f (x) = 4 sin^{5} (x)

\frac{10 sin ^{4} ( x ) cos ( x )}{x}

Solution steps

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

Take the constant out:

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

= 4 \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}

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

Simplify

4 \cdot 5 sin^{4} (x) \frac{cos ( x )}{2 x} : \frac{10 sin ^{4} ( x ) cos ( x )}{x}

= \frac{10 sin ^{4} ( x ) cos ( x )}{x}

\frac{d}{d x} ((x - 2) (2 x - 3))

\frac{d}{d x} (arctan (\frac{40}{x}))

\int 9 x cos (2 x) d x

y = x^{2} - 1, (- 1, 1)

y = x - 6, y^{2} = x

What is the derivative of f(x)=4sin^5(sqrt(x)) ?
The derivative of f(x)=4sin^5(sqrt(x)) is (10sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of f(x)=4sin^5(sqrt(x)) ?
The first derivative of f(x)=4sin^5(sqrt(x)) is (10sin^4(sqrt(x))cos(sqrt(x)))/(sqrt(x))