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Popular >

derivative of (ae^{x/2}/2-be^{-x})

Solution

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

Solution

\frac{a e ^{\frac{x}{2}}}{4} + b e^{- x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{a e ^{\frac{x}{2}}}{2}) = \frac{a e ^{\frac{x}{2}}}{4}

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

= \frac{a e ^{\frac{x}{2}}}{4} - (- b e^{- x})

Simplify

= \frac{a e ^{\frac{x}{2}}}{4} + b e^{- x}

Popular Examples

derivative of 1/(sqrt(-25x^2+2y^2-50))

\frac{d}{d x} (\frac{1}{- 25 x ^{2} + 2 y ^{2} - 50})

limit as x approaches 4 of x+sqrt(x)

x \to 4 lim (x + x)

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y = ln (x x^{2} - 2)

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(6, - 1), (8, 3)

derivative of (ln(x)/(x^{6/5)})

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

Frequently Asked Questions (FAQ)

What is the derivative of (ae^{x/2}/2-be^{-x}) ?
The derivative of (ae^{x/2}/2-be^{-x}) is (ae^{x/2})/4+be^{-x}
What is the first derivative of (ae^{x/2}/2-be^{-x}) ?
The first derivative of (ae^{x/2}/2-be^{-x}) is (ae^{x/2})/4+be^{-x}