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Popular >

derivative of ln(sqrt(x^2+1)+e^{-x^2})

Solution

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

Solution

\frac{x}{x ^{2} + 1} - 2 e^{- x^{2}} x

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{x}{x ^{2} + 1} - 2 e^{- x^{2}} x

Graph

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Frequently Asked Questions (FAQ)

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