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Popular >

derivative of 50e^{-0.5x}-(5/x)

Solution

\frac{d}{d x} (50 e^{- 0.5 x} - (\frac{5}{x}))

Solution

- 25 e^{- 0.5 x} + \frac{5}{x ^{2}}

Solution steps

\frac{d}{d x} (50 e^{- 0.5 x} - (\frac{5}{x}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (50 e^{- 0.5 x}) - \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (50 e^{- 0.5 x}) = - 25 e^{- 0.5 x}

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= - 25 e^{- 0.5 x} - (- \frac{5}{x ^{2}})

Simplify

= - 25 e^{- 0.5 x} + \frac{5}{x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 50e^{-0.5x}-(5/x) ?
The derivative of 50e^{-0.5x}-(5/x) is -25e^{-0.5x}+5/(x^2)
What is the first derivative of 50e^{-0.5x}-(5/x) ?
The first derivative of 50e^{-0.5x}-(5/x) is -25e^{-0.5x}+5/(x^2)