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

The derivative of f(x)=(e^{5x})/(2x-5) is (10e^{5x}x-27e^{5x})/((2x-5)^2)

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

The first derivative of f(x)=(e^{5x})/(2x-5) is (10e^{5x}x-27e^{5x})/((2x-5)^2)

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derivative of

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

\frac{10 e ^{5 x} x - 27 e ^{5 x}}{( 2 x - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

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

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

Expand

e^{5 x} \cdot 5 (2 x - 5) - 2 e^{5 x} : 10 e^{5 x} x - 27 e^{5 x}

= \frac{10 e ^{5 x} x - 27 e ^{5 x}}{( 2 x - 5 ) ^{2}}

What is the derivative of f(x)=(e^{5x})/(2x-5) ?
The derivative of f(x)=(e^{5x})/(2x-5) is (10e^{5x}x-27e^{5x})/((2x-5)^2)
What is the first derivative of f(x)=(e^{5x})/(2x-5) ?
The first derivative of f(x)=(e^{5x})/(2x-5) is (10e^{5x}x-27e^{5x})/((2x-5)^2)