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Popular >

derivative of (sqrt(x)/(7+x))

Solution

\frac{d}{d x} (\frac{x}{7 + x})

Solution

\frac{7 - x}{2 x ( 7 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{7 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x}{( 7 + x ) ^{2}}

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

\frac{d}{d x} (7 + x) = 1

= \frac{\frac{1}{2 x} ( 7 + x ) - 1 \cdot x}{( 7 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 7 + x ) - 1 \cdot x}{( 7 + x ) ^{2}} : \frac{7 - x}{2 x ( 7 + x ) ^{2}}

= \frac{7 - x}{2 x ( 7 + x ) ^{2}}

Popular Examples

derivative of 8/(x^9)

\frac{d}{d x} (\frac{8}{x ^{9}})

(\partial)/(\partial x)((e^x+e^y)^4)

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{4})

derivative of sqrt(7x+9)

\frac{d}{d x} (7 x + 9)

derivative of f(t)=(1+sqrt(t))(2t^2-7)derivative of

f (t) = (1 + t) (2 t^{2} - 7)

integral of x^1((5x^2+2/3)^4)/1

\int x^{1} \frac{( 5 x ^{2} + \frac{2}{3} ) ^{4}}{1} d x

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)/(7+x)) ?
The derivative of (sqrt(x)/(7+x)) is (7-x)/(2sqrt(x)(7+x)^2)
What is the first derivative of (sqrt(x)/(7+x)) ?
The first derivative of (sqrt(x)/(7+x)) is (7-x)/(2sqrt(x)(7+x)^2)