What is the derivative of (e^x/(5x^2+8)) ?

The derivative of (e^x/(5x^2+8)) is (e^x(5x^2+8)-10xe^x)/((5x^2+8)^2)

What is the first derivative of (e^x/(5x^2+8)) ?

The first derivative of (e^x/(5x^2+8)) is (e^x(5x^2+8)-10xe^x)/((5x^2+8)^2)

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\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 8})

\frac{e ^{x} ( 5 x ^{2} + 8 ) - 10 x e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 5 x ^{2} + 8 ) - \frac{d}{d x} ( 5 x ^{2} + 8 ) e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (5 x^{2} + 8) = 10 x

= \frac{e ^{x} ( 5 x ^{2} + 8 ) - 10 x e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}

What is the derivative of (e^x/(5x^2+8)) ?
The derivative of (e^x/(5x^2+8)) is (e^x(5x^2+8)-10xe^x)/((5x^2+8)^2)
What is the first derivative of (e^x/(5x^2+8)) ?
The first derivative of (e^x/(5x^2+8)) is (e^x(5x^2+8)-10xe^x)/((5x^2+8)^2)