en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^3+5)ex

Solution

derivative of

(x^{3} + 5) e x

Solution

e (4 x^{3} + 5)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

\frac{d x}{d x} = 1

= e (3 x^{2} x + 1 \cdot (x^{3} + 5))

Simplify

e (3 x^{2} x + 1 \cdot (x^{3} + 5)) : e (4 x^{3} + 5)

= e (4 x^{3} + 5)

Popular Examples

integral of (x^4)/(x+4)

\int \frac{x ^{4}}{x + 4} d x

(\partial)/(\partial z)((e^{xz+y})/(z^2+w))

\frac{\partial}{\partial z} (\frac{e ^{x z + y}}{z ^{2} + w})

derivative of sin(t)derivative of

sin (t)

integral of ln(x^3)

\int ln (x^{3}) d x

derivative of 7e^x(sqrt(x))

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+5)ex ?
The derivative of (x^3+5)ex is e(4x^3+5)
What is the first derivative of (x^3+5)ex ?
The first derivative of (x^3+5)ex is e(4x^3+5)