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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

50 e^{- 0.5 x - \frac{5}{x}} (- 0.5 + \frac{5}{x ^{2}})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- 0.5 x - \frac{5}{x}) = - 0.5 + \frac{5}{x ^{2}}

= 50 e^{- 0.5 x - \frac{5}{x}} (- 0.5 + \frac{5}{x ^{2}})

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