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Popular >

derivative of (1/2 x)^3

Solution

derivative of

(\frac{1}{2} x)^{3}

Solution

\frac{3 x ^{2}}{8}

Solution steps

\frac{d}{d x} ((\frac{1}{2} x)^{3})

Apply the chain rule:

3 (\frac{1}{2} x)^{2} \frac{d}{d x} (\frac{1}{2} x)

= 3 (\frac{1}{2} x)^{2} \frac{d}{d x} (\frac{1}{2} x)

\frac{d}{d x} (\frac{1}{2} x) = \frac{1}{2}

= 3 (\frac{1}{2} x)^{2} \frac{1}{2}

Simplify

3 (\frac{1}{2} x)^{2} \frac{1}{2} : \frac{3 x ^{2}}{8}

= \frac{3 x ^{2}}{8}

Popular Examples

derivative of (3x^2+4x+1^{10})

\frac{d}{d x} ((3 x^{2} + 4 x + 1)^{10})

integral from 4 to 8 of x/(x^2+6x+13)

\int_{4}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

derivative of 1/a sin(b+ax)

\frac{d}{d x} (\frac{1}{a} sin (b + a x))

integral of e^{5x}cos(x)

\int e^{5 x} cos (x) d x

(dy)/(dx)=(((2y+5))/(8x+9))^2

\frac{d y}{d x} = (\frac{( 2 y + 5 )}{8 x + 9})^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (1/2 x)^3 ?
The derivative of (1/2 x)^3 is (3x^2)/8
What is the first derivative of (1/2 x)^3 ?
The first derivative of (1/2 x)^3 is (3x^2)/8