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Popular >

derivative of (sqrt(x)/(6+x))

Solution

\frac{d}{d x} (\frac{x}{6 + x})

Solution

\frac{6 - x}{2 x ( 6 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{6 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( 6 + x ) - \frac{d}{d x} ( 6 + x ) x}{( 6 + x ) ^{2}}

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

\frac{d}{d x} (6 + x) = 1

= \frac{\frac{1}{2 x} ( 6 + x ) - 1 \cdot x}{( 6 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 6 + x ) - 1 \cdot x}{( 6 + x ) ^{2}} : \frac{6 - x}{2 x ( 6 + x ) ^{2}}

= \frac{6 - x}{2 x ( 6 + x ) ^{2}}

Popular Examples

(\partial)/(\partial x)(1/(2+xy^2))

\frac{\partial}{\partial x} (\frac{1}{2 + x y ^{2}})

limit as x approaches 0 of (x-sqrt(x))/x

x \to 0 lim (\frac{x - x}{x})

derivative of (x^2+2^2)

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

(\partial)/(\partial y)(2xyln(y))

\frac{\partial}{\partial y} (2 x y ln (y))

simplify 5/12 (3+sqrt(5))x^3 simplify

\frac{5}{12} (3 + 5) x^{3}

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)/(6+x)) ?
The derivative of (sqrt(x)/(6+x)) is (6-x)/(2sqrt(x)(6+x)^2)
What is the first derivative of (sqrt(x)/(6+x)) ?
The first derivative of (sqrt(x)/(6+x)) is (6-x)/(2sqrt(x)(6+x)^2)