en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (e^x/(7x^2+8))

Solution

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 8})

Solution

\frac{e ^{x} ( 7 x ^{2} + 8 ) - 14 x e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 7 x ^{2} + 8 ) - \frac{d}{d x} ( 7 x ^{2} + 8 ) e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 8) = 14 x

= \frac{e ^{x} ( 7 x ^{2} + 8 ) - 14 x e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

Popular Examples

integral from 0 to 5 of |x-3|

\int_{0}^{5} ∣ x - 3 ∣ d x

integral of x13^x

\int x 1 3^{x} d x

integral of y^2sinh(5y)

\int y^{2} sinh (5 y) d y

integral from 0 to 1 of integral from 0 to sqrt(x of)(4-2y)/((1+x)^2)

\int_{0}^{1} \int_{0}^{x} \frac{4 - 2 y}{( 1 + x ) ^{2}} d y d x

integral from 0 to pi/(24) of cos(6x)

\int_{0}^{\frac{π}{24}} cos (6 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(7x^2+8)) ?
The derivative of (e^x/(7x^2+8)) is (e^x(7x^2+8)-14xe^x)/((7x^2+8)^2)
What is the first derivative of (e^x/(7x^2+8)) ?
The first derivative of (e^x/(7x^2+8)) is (e^x(7x^2+8)-14xe^x)/((7x^2+8)^2)