What is the derivative of 2sin^3(sqrt(x)) ?

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

What is the first derivative of 2sin^3(sqrt(x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x^{2} sin^{4} (x) + x cos^{- 2} (x)

\int cos (x) tan^{2} (x) d x

y^{^{'}} = - 2 y, y (0) = 2

\frac{\partial}{\partial y} (x y e^{5 y})

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