What is the derivative of (e^{x^2}+3e^x/(e^x)) ?

The derivative of (e^{x^2}+3e^x/(e^x)) is e^{x^2-x}(2x-1)

What is the first derivative of (e^{x^2}+3e^x/(e^x)) ?

The first derivative of (e^{x^2}+3e^x/(e^x)) is e^{x^2-x}(2x-1)

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

e^{x^{2} - x} (2 x - 1)

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (e^{x^{2}} + 3 e^{x}) = e^{x^{2}} \cdot 2 x + 3 e^{x}

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

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

Simplify

\frac{( e ^{x^{2}} \cdot 2 x + 3 e ^{x} ) e ^{x} - e ^{x} ( e ^{x^{2}} + 3 e ^{x} )}{( e ^{x} ) ^{2}} : e^{x^{2} - x} (2 x - 1)

= e^{x^{2} - x} (2 x - 1)

What is the derivative of (e^{x^2}+3e^x/(e^x)) ?
The derivative of (e^{x^2}+3e^x/(e^x)) is e^{x^2-x}(2x-1)
What is the first derivative of (e^{x^2}+3e^x/(e^x)) ?
The first derivative of (e^{x^2}+3e^x/(e^x)) is e^{x^2-x}(2x-1)