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/(5x^2+9))

Solution

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 9})

Solution

\frac{e ^{x} ( 5 x ^{2} + 9 ) - 10 x e ^{x}}{( 5 x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 9})

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} + 9 ) - \frac{d}{d x} ( 5 x ^{2} + 9 ) e ^{x}}{( 5 x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (5 x^{2} + 9) = 10 x

= \frac{e ^{x} ( 5 x ^{2} + 9 ) - 10 x e ^{x}}{( 5 x ^{2} + 9 ) ^{2}}

Graph

Popular Examples

integral of (2x+7)/((x-1)^2(x+1))

\int \frac{2 x + 7}{( x - 1 ) ^{2} ( x + 1 )} d x

integral from 1 to 2 of 18x^24^{x^3}

\int_{1}^{2} 18 x^{2} 4^{x^{3}} d x

integral of (x^2)/(sqrt(x+1))

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

limit as x approaches 0-of 1+e^{1/x}

x \to 0 - lim (1 + e^{\frac{1}{x}})

laplacetransform 3t^2+15t+15 laplace transform

3 t^{2} + 15 t + 15

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(5x^2+9)) ?
The derivative of (e^x/(5x^2+9)) is (e^x(5x^2+9)-10xe^x)/((5x^2+9)^2)
What is the first derivative of (e^x/(5x^2+9)) ?
The first derivative of (e^x/(5x^2+9)) is (e^x(5x^2+9)-10xe^x)/((5x^2+9)^2)