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Popular >

derivative of ae^{x/2}+be^{-x}

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

integral of 1/2 (1-cos(x))^2

\int \frac{1}{2} (1 - cos (x))^{2} d x

integral from 0 to 1 of xsqrt(4+5x)

\int_{0}^{1} x 4 + 5 x d x

derivative of cos(xln(x^2+1)-ln(x^4+1))

\frac{d}{d x} (cos (x) ln (x^{2} + 1) - ln (x^{4} + 1))

y^'=-y^3,y(0)=a

y^{^{'}} = - y^{3}, y (0) = a

taylor 1+x^2 taylor

1 + x^{2}

Frequently Asked Questions (FAQ)

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