en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(6x^2+4)e^x

Solution

derivative of

f (x) = (6 x^{2} + 4) e^{x}

Solution

12 x e^{x} + e^{x} (6 x^{2} + 4)

Solution steps

\frac{d}{d x} ((6 x^{2} + 4) e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 6 x^{2} + 4, g = e^{x}

= \frac{d}{d x} (6 x^{2} + 4) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} + 4)

\frac{d}{d x} (6 x^{2} + 4) = 12 x

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

= 12 x e^{x} + e^{x} (6 x^{2} + 4)

Popular Examples

integral of x/(x^2+6x+11)

\int \frac{x}{x ^{2} + 6 x + 11} d x

derivative of (5-3x^3)

\frac{d}{d x} ((5 - 3 x)^{3})

derivative of e^{6e^x}derivative of

e^{6 e^{x}}

integral from 0 to 1 of (2x-2x^2)

\int_{0}^{1} (2 x - 2 x^{2}) d x

derivative of x^4+x^3+x^2+1

\frac{d}{d x} (x^{4} + x^{3} + x^{2} + 1)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(6x^2+4)e^x ?
The derivative of f(x)=(6x^2+4)e^x is 12xe^x+e^x(6x^2+4)
What is the first derivative of f(x)=(6x^2+4)e^x ?
The first derivative of f(x)=(6x^2+4)e^x is 12xe^x+e^x(6x^2+4)