What is the derivative of e^x(3x^2-x+1) ?

The derivative of e^x(3x^2-x+1) is 3e^xx^2+5e^xx

What is the first derivative of e^x(3x^2-x+1) ?

The first derivative of e^x(3x^2-x+1) is 3e^xx^2+5e^xx

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

e^{x} (3 x^{2} - x + 1)

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = 3 x^{2} - x + 1

= \frac{d}{d x} (e^{x}) (3 x^{2} - x + 1) + \frac{d}{d x} (3 x^{2} - x + 1) e^{x}

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

\frac{d}{d x} (3 x^{2} - x + 1) = 6 x - 1

= e^{x} (3 x^{2} - x + 1) + (6 x - 1) e^{x}

Simplify

e^{x} (3 x^{2} - x + 1) + (6 x - 1) e^{x} : 3 e^{x} x^{2} + 5 e^{x} x

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

\frac{\partial}{\partial y} (e^{- x y^{2}} + y^{3} x^{4})

x y

n = 1 \sum \infty n^{3} + n

(x^{5})^{^{'}}

\int \frac{1}{4 x + 9} d x

What is the derivative of e^x(3x^2-x+1) ?
The derivative of e^x(3x^2-x+1) is 3e^xx^2+5e^xx
What is the first derivative of e^x(3x^2-x+1) ?
The first derivative of e^x(3x^2-x+1) is 3e^xx^2+5e^xx