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

The derivative of (e^x)/(5x-2) is (5e^xx-7e^x)/((5x-2)^2)

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

The first derivative of (e^x)/(5x-2) is (5e^xx-7e^x)/((5x-2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{e ^{x}}{5 x - 2}

\frac{5 e ^{x} x - 7 e ^{x}}{( 5 x - 2 ) ^{2}}

Solution steps

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

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

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

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

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

Expand

e^{x} (5 x - 2) - 5 e^{x} : 5 e^{x} x - 7 e^{x}

= \frac{5 e ^{x} x - 7 e ^{x}}{( 5 x - 2 ) ^{2}}

\int_{0}^{2 π} sin^{2} (9 x) d x

4 t

x \to 0 lim (ln (1 + sin (x)))

\frac{d y}{d x} = x^{7} y

\frac{d}{d x} (ln (sinh (x)))

What is the derivative of (e^x)/(5x-2) ?
The derivative of (e^x)/(5x-2) is (5e^xx-7e^x)/((5x-2)^2)
What is the first derivative of (e^x)/(5x-2) ?
The first derivative of (e^x)/(5x-2) is (5e^xx-7e^x)/((5x-2)^2)