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Popular >

d/(ds)(ln(1+1/(s^2)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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\int (2^{x} + x)^{2} d x

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\int cos (\frac{π x}{2}) d x

(dy)/(dx)=16xsec^2(4x)

\frac{d y}{d x} = 16 x sec^{2} (4 x)

derivative of ysinh(x^2)

\frac{d}{d x} (y sinh (x^{2}))

derivative of log_{2}(x^{2x})

\frac{d}{d x} (lo g_{2} (x^{2 x}))

Frequently Asked Questions (FAQ)

What is the d/(ds)(ln(1+1/(s^2))) ?
The d/(ds)(ln(1+1/(s^2))) is -2/(s(s^2+1))
What is the first d/(ds)(ln(1+1/(s^2))) ?
The first d/(ds)(ln(1+1/(s^2))) is -2/(s(s^2+1))