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Popular >

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

Solution

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

Solution

\frac{x + 10}{2 ( x + 5 ) x + 5}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot x + 5 - \frac{1}{2 x + 5} x}{( x + 5 ) ^{2}} : \frac{x + 10}{2 ( x + 5 ) x + 5}

= \frac{x + 10}{2 ( x + 5 ) x + 5}

Graph

Popular Examples

x(dy)/(dx)=y(y+1)

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

tangent of f(x)=(6x)/(x+2),(4,4)tangent of

f (x) = \frac{6 x}{x + 2}, (4, 4)

derivative of f(x)=-1/6 (x^{-6}+x^{12})derivative of

f (x) = - \frac{1}{6} (x^{- 6} + x^{12})

derivative of (x^2-36)/(x-6)derivative of

\frac{x ^{2} - 36}{x - 6}

y^{''}+y=sin(2x)

y^{^{''}} + y = sin (2 x)

Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(x+5)) ?
The derivative of x/(sqrt(x+5)) is (x+10)/(2(x+5)sqrt(x+5))
What is the first derivative of x/(sqrt(x+5)) ?
The first derivative of x/(sqrt(x+5)) is (x+10)/(2(x+5)sqrt(x+5))