What is the derivative of (e^x)/(5x+3) ?

The derivative of (e^x)/(5x+3) is (5e^xx-2e^x)/((5x+3)^2)

What is the first derivative of (e^x)/(5x+3) ?

The first derivative of (e^x)/(5x+3) is (5e^xx-2e^x)/((5x+3)^2)

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derivative of

\frac{e ^{x}}{5 x + 3}

\frac{5 e ^{x} x - 2 e ^{x}}{( 5 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 x + 3})

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

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

\frac{d}{d x} (5 x + 3) = 5

= \frac{e ^{x} ( 5 x + 3 ) - 5 e ^{x}}{( 5 x + 3 ) ^{2}}

Expand

e^{x} (5 x + 3) - 5 e^{x} : 5 e^{x} x - 2 e^{x}

= \frac{5 e ^{x} x - 2 e ^{x}}{( 5 x + 3 ) ^{2}}

What is the derivative of (e^x)/(5x+3) ?
The derivative of (e^x)/(5x+3) is (5e^xx-2e^x)/((5x+3)^2)
What is the first derivative of (e^x)/(5x+3) ?
The first derivative of (e^x)/(5x+3) is (5e^xx-2e^x)/((5x+3)^2)