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Popular >

derivative of x/(sqrt(x+3))

Solution

\frac{d}{d x} (\frac{x}{x + 3})

Solution

\frac{x + 6}{2 ( x + 3 ) x + 3}

Solution steps

\frac{d}{d x} (\frac{x}{x + 3})

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot x + 3 - \frac{1}{2 x + 3} x}{( x + 3 ) ^{2}}

Simplify

\frac{1 \cdot x + 3 - \frac{1}{2 x + 3} x}{( x + 3 ) ^{2}} : \frac{x + 6}{2 ( x + 3 ) x + 3}

= \frac{x + 6}{2 ( x + 3 ) x + 3}

Graph

Popular Examples

limit as x approaches 0 of-x^2sin(3x)

x \to 0 lim (- x^{2} sin (3 x))

inverse oflaplace s/((s^2+9)(s^2+16))inverse laplace

\frac{s}{( s ^{2} + 9 ) ( s ^{2} + 16 )}

integral of (sqrt(x))/2

\int \frac{x}{2} d x

y^{''}+5y+349/4 y=0,y(0)=-5,y^'(0)=-29/2

y^{^{''}} + 5 y + \frac{349}{4} y = 0, y (0) = - 5, y^{^{'}} (0) = - \frac{29}{2}

derivative of (x^3+2^3)

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

Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(x+3)) ?
The derivative of x/(sqrt(x+3)) is (x+6)/(2(x+3)sqrt(x+3))
What is the first derivative of x/(sqrt(x+3)) ?
The first derivative of x/(sqrt(x+3)) is (x+6)/(2(x+3)sqrt(x+3))