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Popular Calculus >

derivative of (sqrt(x)/(1+x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (7(sin(2x))/(sin(x)))

\int (7 \frac{sin ( 2 x )}{sin ( x )}) d x

integral of (3x^2+14x)(x^3+7x^2+1)

\int (3 x^{2} + 14 x) (x^{3} + 7 x^{2} + 1) d x

tangent of sqrt((5x^2-3x+2))^7

t an g e n t (5 x^{2} - 3 x + 2)^{7}

(\partial)/(\partial x)(ln(7x))

\frac{\partial}{\partial x} (ln (7 x))

x^{''}+3x^'=0,x(0)=0,x^'(0)=-3

x^{^{''}} + 3 x^{^{'}} = 0, x (0) = 0, x^{^{'}} (0) = - 3

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)/(1+x)) ?
The derivative of (sqrt(x)/(1+x)) is (1-x)/(2sqrt(x)(1+x)^2)
What is the first derivative of (sqrt(x)/(1+x)) ?
The first derivative of (sqrt(x)/(1+x)) is (1-x)/(2sqrt(x)(1+x)^2)