What is 1/2 (x^2+1)^{-1/2}(2x) ?

The solution to 1/2 (x^2+1)^{-1/2}(2x) is x/((x^2+1)^{1/2)}

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simplify 1/2 (x^2+1)^{-1/2}(2x)

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

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

Cancel the common factor:

2

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

Multiply:

1 \cdot 1 \cdot x = x

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

e^{- l n (x)} x

e^{- 2} \cdot 2^{0} \cdot \frac{1}{0 !} \cdot 0.125

(- 3 e^{- 2 (t - x)} + 10 e^{- t + x}) \cdot e^{- 2 x}

(- 1)^{n} \cdot 3^{n}

3^{- 3}

What is 1/2 (x^2+1)^{-1/2}(2x) ?
The solution to 1/2 (x^2+1)^{-1/2}(2x) is x/((x^2+1)^{1/2)}