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

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

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

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

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derivative of

\frac{1}{1 + s ^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 8 t^{3} - 6 t^{- 2} d t

x \to 5 + lim (\frac{2}{x - 5})

\int (e^{x} - 1)^{3} d x

f (x) = sin (5 x^{2})

x \to 0 lim (e^{x (1 - s)})

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