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Popular >

derivative of sqrt(x/(2+cx))

Solution

\frac{d}{d x} (\frac{x}{2 + c x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{2 + c x})

Apply the chain rule:

\frac{1}{2 \frac{x}{2 + c x}} \frac{d}{d x} (\frac{x}{2 + c x})

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

\frac{d}{d x} (\frac{x}{2 + c x}) = \frac{2}{( 2 + c x ) ^{2}}

= \frac{1}{2 \frac{x}{2 + c x}} \cdot \frac{2}{( 2 + c x ) ^{2}}

Simplify

\frac{1}{2 \frac{x}{2 + c x}} \cdot \frac{2}{( 2 + c x ) ^{2}} : \frac{1}{x ( c x + 2 ) ^{\frac{3}{2}}}

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

Popular Examples

integral of (sqrt(1-x^2))/(x^2)

\int \frac{1 - x ^{2}}{x ^{2}} d x

integral of 2/((x-3)(x+1))

\int \frac{2}{( x - 3 ) ( x + 1 )} d x

integral from 1 to infinity of 9/(x^2+1)

\int_{1}^{\infty} \frac{9}{x ^{2} + 1} d x

integral of (4x+3)(2x^2+3x)^3

\int (4 x + 3) (2 x^{2} + 3 x)^{3} d x

integral of 1/(6(x^2+1))

\int \frac{1}{6 ( x ^{2} + 1 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x/(2+cx)) ?
The derivative of sqrt(x/(2+cx)) is 1/(sqrt(x)(cx+2)^{3/2)}
What is the first derivative of sqrt(x/(2+cx)) ?
The first derivative of sqrt(x/(2+cx)) is 1/(sqrt(x)(cx+2)^{3/2)}