What is the derivative of f(x)=(x^3+5)e^x ?

The derivative of f(x)=(x^3+5)e^x is 3x^2e^x+e^x(x^3+5)

What is the first derivative of f(x)=(x^3+5)e^x ?

The first derivative of f(x)=(x^3+5)e^x is 3x^2e^x+e^x(x^3+5)

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} + 5) e^{x}

3 x^{2} e^{x} + e^{x} (x^{3} + 5)

Solution steps

\frac{d}{d x} ((x^{3} + 5) e^{x})

Apply the Product Rule:

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

f = x^{3} + 5, g = e^{x}

= \frac{d}{d x} (x^{3} + 5) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 5)

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

\int_{- \infty}^{0} e^{- 2 x} d x

y^{^{''}} + 10 y^{^{'}} + 21 y = 0

(9 x + 2)^{\frac{2}{3}}

\int (4 x + 2) (x - 1) d x

y^{^{'}} + y = 5 x y^{3}

What is the derivative of f(x)=(x^3+5)e^x ?
The derivative of f(x)=(x^3+5)e^x is 3x^2e^x+e^x(x^3+5)
What is the first derivative of f(x)=(x^3+5)e^x ?
The first derivative of f(x)=(x^3+5)e^x is 3x^2e^x+e^x(x^3+5)