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

The derivative of ((x+1^2)/(1+x^2)) is (-2x^2+2)/((1+x^2)^2)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 (x + 1) (1 + x^{2}) - 2 x (x + 1)^{2} : - 2 x^{2} + 2

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

\int (e^{x} + 1)^{2} e^{x} d x

4 x + 12, 8 - x^{2}, x = - 2, x = 6

\frac{d y}{d x} = x + 3 y

\int_{- \infty}^{16} r e^{\frac{r}{4}} d r

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

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