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Popular >

derivative of f(x)=sqrt(x/(x+5))

Solution

derivative of

f (x) = \frac{x}{x + 5}

Solution

\frac{5}{2 x ( x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 5})

Apply the chain rule:

\frac{1}{2 \frac{x}{x + 5}} \frac{d}{d x} (\frac{x}{x + 5})

= \frac{1}{2 \frac{x}{x + 5}} \frac{d}{d x} (\frac{x}{x + 5})

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

= \frac{1}{2 \frac{x}{x + 5}} \cdot \frac{5}{( x + 5 ) ^{2}}

Simplify

\frac{1}{2 \frac{x}{x + 5}} \cdot \frac{5}{( x + 5 ) ^{2}} : \frac{5}{2 x ( x + 5 ) ^{\frac{3}{2}}}

= \frac{5}{2 x ( x + 5 ) ^{\frac{3}{2}}}

Popular Examples

tangent of y=sqrt(9-4x),\at x=-1 tangent of

y = 9 - 4 x, at x = - 1

integral from 0 to pi/4 of 9tan^3(x)

\int_{0}^{\frac{π}{4}} 9 tan^{3} (x) d x

derivative of (5x^4+3x^3/(4x-9))

\frac{d}{d x} (\frac{5 x ^{4} + 3 x ^{3}}{4 x - 9})

maclaurin e^xsin(x)maclaurin

e^{x} sin (x)

integral of (5-e^x)/(e^{2x)}

\int \frac{5 - e ^{x}}{e ^{2 x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x/(x+5)) ?
The derivative of f(x)=sqrt(x/(x+5)) is 5/(2sqrt(x)(x+5)^{3/2)}
What is the first derivative of f(x)=sqrt(x/(x+5)) ?
The first derivative of f(x)=sqrt(x/(x+5)) is 5/(2sqrt(x)(x+5)^{3/2)}