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Popular >

derivative of 4e^{x/2}-3e^{-x}

Solution

\frac{d}{d x} (4 e^{\frac{x}{2}} - 3 e^{- x})

Solution

2 e^{\frac{x}{2}} + 3 e^{- x}

Solution steps

\frac{d}{d x} (4 e^{\frac{x}{2}} - 3 e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 e^{\frac{x}{2}}) - \frac{d}{d x} (3 e^{- x})

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

\frac{d}{d x} (3 e^{- x}) = - 3 e^{- x}

= 2 e^{\frac{x}{2}} - (- 3 e^{- x})

Simplify

= 2 e^{\frac{x}{2}} + 3 e^{- x}

Popular Examples

integral from 0 to pi/2 of xsin(8x)

\int_{0}^{\frac{π}{2}} x sin (8 x) d x

limit as x approaches-0 of ((x+2)^2-4)/x

x \to - 0 lim (\frac{( x + 2 ) ^{2} - 4}{x})

derivative of f(x)= 2/((3x^2+7)^2)derivative of

f (x) = \frac{2}{( 3 x ^{2} + 7 ) ^{2}}

tangent of f(x)=6x-x^2 tangent of

f (x) = 6 x - x^{2}

8-x^2,x^2,x=-3,x=3

8 - x^{2}, x^{2}, x = - 3, x = 3

Frequently Asked Questions (FAQ)

What is the derivative of 4e^{x/2}-3e^{-x} ?
The derivative of 4e^{x/2}-3e^{-x} is 2e^{x/2}+3e^{-x}
What is the first derivative of 4e^{x/2}-3e^{-x} ?
The first derivative of 4e^{x/2}-3e^{-x} is 2e^{x/2}+3e^{-x}