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Popular >

derivative of f(0)= x/(x^2+1)

Solution

derivative of

f (0) = \frac{x}{x ^{2} + 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

integral of e^{-0.01t}

\int e^{- 0.01 t} d t

derivative of 1/(1+|x|+1/(1+|x-3|))

\frac{d}{d x} (\frac{1}{1 + ∣ x ∣} + \frac{1}{1 + ∣ x - 3 ∣})

(\partial)/(\partial y)(2x-3yz)

\frac{\partial}{\partial y} (2 x - 3 yz)

d/(d{r)}((200{r}({r}+2))/((2+3{r))^2})

\frac{d}{d r} (\frac{200 r ( r + 2 )}{( 2 + 3 r ) ^{2}})

tangent of y=sqrt(9-10x),\at x=-1 tangent of

y = 9 - 10 x, at x = - 1

Frequently Asked Questions (FAQ)

What is the derivative of f(0)= x/(x^2+1) ?
The derivative of f(0)= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)
What is the first derivative of f(0)= x/(x^2+1) ?
The first derivative of f(0)= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)