en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (3x^2-5xe^x)

Solution

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

Solution

3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Solution steps

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

Apply the Product Rule:

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

f = 3 x^{2} - 5 x, g = e^{x}

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

\frac{d}{d x} (3 x^{2} - 5 x) = 6 x - 5

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

= (6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x)

Simplify

(6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x) : 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

= 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Popular Examples

integral of x/(x-1)

\int \frac{x}{x - 1} d x

derivative of y=(e^x)/(5x^2)derivative of

y = \frac{e ^{x}}{5 x ^{2}}

derivative of (2x+3^{1.4})

\frac{d}{d x} ((2 x + 3)^{1.4})

(\partial)/(\partial x)(x+y^{1/2})

\frac{\partial}{\partial x} (x + y^{\frac{1}{2}})

limit as x approaches 0 of tan(7x)

x \to 0 lim (tan (7 x))

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-5xe^x) ?
The derivative of (3x^2-5xe^x) is 3e^xx^2+e^xx-5e^x
What is the first derivative of (3x^2-5xe^x) ?
The first derivative of (3x^2-5xe^x) is 3e^xx^2+e^xx-5e^x