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

The derivative of 2/(sqrt(x^2+1)) is -(2x)/((x^2+1)^{3/2)}

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

The first derivative of 2/(sqrt(x^2+1)) is -(2x)/((x^2+1)^{3/2)}

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

- \frac{2 x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 1)

= - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 1)

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

= 2 (- \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 x)

Simplify

2 (- \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 x) : - \frac{2 x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

= - \frac{2 x}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

\int_{0}^{2} 2 π (5 - x) (8 - x^{3}) d x

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\int - 16 cos (4 t + π) d t

What is the derivative of 2/(sqrt(x^2+1)) ?
The derivative of 2/(sqrt(x^2+1)) is -(2x)/((x^2+1)^{3/2)}
What is the first derivative of 2/(sqrt(x^2+1)) ?
The first derivative of 2/(sqrt(x^2+1)) is -(2x)/((x^2+1)^{3/2)}