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)/(4x^2+3)

Solution

derivative of

\frac{e ^{x}}{4 x ^{2} + 3}

Solution

\frac{e ^{x} ( 4 x ^{2} + 3 ) - 8 x e ^{x}}{( 4 x ^{2} + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2} + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 4 x ^{2} + 3 ) - \frac{d}{d x} ( 4 x ^{2} + 3 ) e ^{x}}{( 4 x ^{2} + 3 ) ^{2}}

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

= \frac{e ^{x} ( 4 x ^{2} + 3 ) - 8 x e ^{x}}{( 4 x ^{2} + 3 ) ^{2}}

Popular Examples

derivative of f(x)=2pir^2+(1000)/r derivative of

f (x) = 2 π r^{2} + \frac{1000}{r}

tangent of y= 6/(sqrt(x)),(36, 6/6)tangent of

y = \frac{6}{x}, (36, \frac{6}{6})

(dy)/(dx)=-2y+e^x

\frac{d y}{d x} = - 2 y + e^{x}

integral from 0 to pi/6 of 4cos^5(3x)

\int_{0}^{\frac{π}{6}} 4 cos^{5} (3 x) d x

integral of 2/x+3sin(x)-4e^x

\int \frac{2}{x} + 3 sin (x) - 4 e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x)/(4x^2+3) ?
The derivative of (e^x)/(4x^2+3) is (e^x(4x^2+3)-8xe^x)/((4x^2+3)^2)
What is the first derivative of (e^x)/(4x^2+3) ?
The first derivative of (e^x)/(4x^2+3) is (e^x(4x^2+3)-8xe^x)/((4x^2+3)^2)