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

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

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simplify 1/2*(t^2+1)^{-1/2}(2t)

simplify

\frac{1}{2} \cdot (t^{2} + 1)^{- \frac{1}{2}} (2 t)

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

Solution steps

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

Apply exponent rule:

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

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

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

Cancel the common factor:

2

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

Multiply:

1 \cdot 1 \cdot t = t

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

(e^{- x}) (- e^{- x})

9 e^{- 6^{2}}

(2 + 3) (2 - 3)

x^{9}

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