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Popular >

derivative of 3sin^3(sqrt(x))

Solution

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

Solution

\frac{9 sin ^{2} ( x ) cos ( x )}{2 x}

Solution steps

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

Take the constant out:

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

= 3 \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}

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

Simplify

3 \cdot 3 sin^{2} (x) \frac{cos ( x )}{2 x} : \frac{9 sin ^{2} ( x ) cos ( x )}{2 x}

= \frac{9 sin ^{2} ( x ) cos ( x )}{2 x}

Popular Examples

(\partial)/(\partial x)(ln(x+5y+3z))

\frac{\partial}{\partial x} (ln (x + 5 y + 3 z))

(\partial)/(\partial x)(x^3+3xy^2-3x)

\frac{\partial}{\partial x} (x^{3} + 3 x y^{2} - 3 x)

integral from 2.5 to 0.5 of (23.75-7.5v)

\int_{2.5}^{0.5} (23.75 - 7.5 v) d v

(\partial)/(\partial y)(8x-(x+y)^3)

\frac{\partial}{\partial y} (8 x - (x + y)^{3})

derivative of sqrt(1/(x^{31)})

\frac{d}{d x} (\frac{1}{x ^{31}})

Frequently Asked Questions (FAQ)

What is the derivative of 3sin^3(sqrt(x)) ?
The derivative of 3sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(2sqrt(x))
What is the first derivative of 3sin^3(sqrt(x)) ?
The first derivative of 3sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(2sqrt(x))