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)=(x^3+7)e^x

Solution

derivative of

f (x) = (x^{3} + 7) e^{x}

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 7)

Solution steps

\frac{d}{d x} ((x^{3} + 7) e^{x})

Apply the Product Rule:

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

f = x^{3} + 7, g = e^{x}

= \frac{d}{d x} (x^{3} + 7) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 7)

\frac{d}{d x} (x^{3} + 7) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 7)

Popular Examples

integral of (2x)/(x^2+14x+49)

\int \frac{2 x}{x ^{2} + 14 x + 49} d x

sum from n=1 to infinity}\sqrt{5 of*2/n

n = 1 \sum \infty 5 \cdot \frac{2}{n}

limit as x approaches 6 of (x^2-9x+18)/(x-6)

x \to 6 lim (\frac{x ^{2} - 9 x + 18}{x - 6})

area y=6x,y= 3/2 x,y=7-x^2 area

y = 6 x, y = \frac{3}{2} x, y = 7 - x^{2}

derivative of 2^{3^{4^x}}

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^3+7)e^x ?
The derivative of f(x)=(x^3+7)e^x is 3x^2e^x+e^x(x^3+7)
What is the first derivative of f(x)=(x^3+7)e^x ?
The first derivative of f(x)=(x^3+7)e^x is 3x^2e^x+e^x(x^3+7)