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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{5}{s ^{2} + 12}

\int sin^{3} (2 a x) cos (2 a x) d x

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

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

\frac{d y}{d t} = y^{3} - y

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