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

The (x/(x^2+1))^' is (-x^2+1)/((x^2+1)^2)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

x^{'} = 1

(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}}

\int cos (x) sin (x) e^{- 2 c o s (x)} d x

y^{^{'}} = 2 x (x - 4)

x \to π + lim (csc (x))

\int tan^{2} (t) d t

\int \frac{x ^{3} + 93 x + 70}{x ^{3} + 100 x} d x

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