en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (7x^2-14x+14)e^x

Solution

derivative of

(7 x^{2} - 14 x + 14) e^{x}

Solution

7 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

Apply the Product Rule:

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

f = 7 x^{2} - 14 x + 14, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 14 x + 14) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 14 x + 14)

\frac{d}{d x} (7 x^{2} - 14 x + 14) = 14 x - 14

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

= (14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14)

Simplify

(14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14) : 7 e^{x} x^{2}

= 7 e^{x} x^{2}

Popular Examples

(\partial)/(\partial y)(y^2sin(x))

\frac{\partial}{\partial y} (y^{2} sin (x))

derivative of ln(sqrt((9-x^2/(9+x^2))))

\frac{d}{d x} (ln (\frac{9 - x ^{2}}{9 + x ^{2}}))

y^{^{'}} = x y - 3 y

limit as x approaches 8 of x^{2/3}

x \to 8 lim (x^{\frac{2}{3}})

(d^2)/(dy^2)(ln(sqrt(x^2+y^2)))

\frac{d ^{2}}{d y ^{2}} (ln (x^{2} + y^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of (7x^2-14x+14)e^x ?
The derivative of (7x^2-14x+14)e^x is 7e^xx^2
What is the first derivative of (7x^2-14x+14)e^x ?
The first derivative of (7x^2-14x+14)e^x is 7e^xx^2