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Popular >

derivative of (sqrt(x)/(9+x))

Solution

\frac{d}{d x} (\frac{x}{9 + x})

Solution

\frac{9 - x}{2 x ( 9 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{9 + x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ) ( 9 + x ) - \frac{d}{d x} ( 9 + x ) x}{( 9 + x ) ^{2}}

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

\frac{d}{d x} (9 + x) = 1

= \frac{\frac{1}{2 x} ( 9 + x ) - 1 \cdot x}{( 9 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 9 + x ) - 1 \cdot x}{( 9 + x ) ^{2}} : \frac{9 - x}{2 x ( 9 + x ) ^{2}}

= \frac{9 - x}{2 x ( 9 + x ) ^{2}}

Popular Examples

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

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

integral of ((e^{2x}))/(4+e^{4x)}

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

\int l d l

limit as x approaches 1 of 9/(x^3-1)

x \to 1 lim (\frac{9}{x ^{3} - 1})

derivative of y=7arctan(x-sqrt(1+x^2))derivative of

y = 7 arctan (x - 1 + x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)/(9+x)) ?
The derivative of (sqrt(x)/(9+x)) is (9-x)/(2sqrt(x)(9+x)^2)
What is the first derivative of (sqrt(x)/(9+x)) ?
The first derivative of (sqrt(x)/(9+x)) is (9-x)/(2sqrt(x)(9+x)^2)