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Popular >

derivative of x/(1+x^2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

integral of (3x-4)/(x^2-x-6)

\int \frac{3 x - 4}{x ^{2} - x - 6} d x

derivative of 6sqrt(x)-3x

\frac{d}{d x} (6 x - 3 x)

limit as x approaches 5-of cx^2+2x

x \to 5 - lim (c x^{2} + 2 x)

integral of (8x^3+7)/((x+1)(2x+1)^3)

\int \frac{8 x ^{3} + 7}{( x + 1 ) ( 2 x + 1 ) ^{3}} d x

area y=(x^2)/2-4x+6,y= x/2-1 area

y = \frac{x ^{2}}{2} - 4 x + 6, y = \frac{x}{2} - 1

Frequently Asked Questions (FAQ)

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