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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Expand

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

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

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