What is the derivative of (8e^{6x}/(5x+2)) ?

The derivative of (8e^{6x}/(5x+2)) is (8(30e^{6x}x+7e^{6x}))/((5x+2)^2)

What is the first derivative of (8e^{6x}/(5x+2)) ?

The first derivative of (8e^{6x}/(5x+2)) is (8(30e^{6x}x+7e^{6x}))/((5x+2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{8 e ^{6 x}}{5 x + 2})

\frac{8 ( 30 e ^{6 x} x + 7 e ^{6 x} )}{( 5 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 e ^{6 x}}{5 x + 2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (\frac{e ^{6 x}}{5 x + 2})

Apply the Quotient Rule:

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

= 8 \cdot \frac{\frac{d}{d x} ( e ^{6 x} ) ( 5 x + 2 ) - \frac{d}{d x} ( 5 x + 2 ) e ^{6 x}}{( 5 x + 2 ) ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= 8 \cdot \frac{e ^{6 x} \cdot 6 ( 5 x + 2 ) - 5 e ^{6 x}}{( 5 x + 2 ) ^{2}}

Simplify

8 \cdot \frac{e ^{6 x} \cdot 6 ( 5 x + 2 ) - 5 e ^{6 x}}{( 5 x + 2 ) ^{2}} : \frac{8 ( 30 e ^{6 x} x + 7 e ^{6 x} )}{( 5 x + 2 ) ^{2}}

= \frac{8 ( 30 e ^{6 x} x + 7 e ^{6 x} )}{( 5 x + 2 ) ^{2}}

\int \frac{1}{2} + \frac{x ^{4}}{4} + \frac{1}{4 x ^{4}} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16

\int_{0}^{10} 1 + 16 x^{2} d x

\int (3 + x^{2})^{\frac{3}{2}} d x

\int_{- π}^{π} cos (2 x) cos (3 x) d x

What is the derivative of (8e^{6x}/(5x+2)) ?
The derivative of (8e^{6x}/(5x+2)) is (8(30e^{6x}x+7e^{6x}))/((5x+2)^2)
What is the first derivative of (8e^{6x}/(5x+2)) ?
The first derivative of (8e^{6x}/(5x+2)) is (8(30e^{6x}x+7e^{6x}))/((5x+2)^2)