What is the derivative of (e^x/(7x^2+9)) ?

The derivative of (e^x/(7x^2+9)) is (e^x(7x^2+9)-14xe^x)/((7x^2+9)^2)

What is the first derivative of (e^x/(7x^2+9)) ?

The first derivative of (e^x/(7x^2+9)) is (e^x(7x^2+9)-14xe^x)/((7x^2+9)^2)

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\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 9})

\frac{e ^{x} ( 7 x ^{2} + 9 ) - 14 x e ^{x}}{( 7 x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 7 x ^{2} + 9 ) - \frac{d}{d x} ( 7 x ^{2} + 9 ) e ^{x}}{( 7 x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 9) = 14 x

= \frac{e ^{x} ( 7 x ^{2} + 9 ) - 14 x e ^{x}}{( 7 x ^{2} + 9 ) ^{2}}

x \to - 7 lim (12)

x^{2} - 8 x + 17

\int (x^{2} + 5) (x - 3) d x

\frac{x}{x ^{2} + 1}

\int e^{- s t} \cdot t^{2} d t

What is the derivative of (e^x/(7x^2+9)) ?
The derivative of (e^x/(7x^2+9)) is (e^x(7x^2+9)-14xe^x)/((7x^2+9)^2)
What is the first derivative of (e^x/(7x^2+9)) ?
The first derivative of (e^x/(7x^2+9)) is (e^x(7x^2+9)-14xe^x)/((7x^2+9)^2)