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Popular >

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}}

Popular Examples

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

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

integral from-5 to 5 of 1/2 (25^2-x^4)

\int_{- 5}^{5} \frac{1}{2} (2 5^{2} - x^{4}) d x

integral of x/(1-x^2+sqrt(1-x^2))

\int \frac{x}{1 - x ^{2} + 1 - x ^{2}} 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

derivative of g(t)=sqrt(1/(t^2-2))derivative of

g (t) = \frac{1}{t ^{2} - 2}

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)