en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(8x^2-16x+16)e^x

Solution

derivative of

y = (8 x^{2} - 16 x + 16) e^{x}

Solution

8 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((8 x^{2} - 16 x + 16) e^{x})

Apply the Product Rule:

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

f = 8 x^{2} - 16 x + 16, g = e^{x}

= \frac{d}{d x} (8 x^{2} - 16 x + 16) e^{x} + \frac{d}{d x} (e^{x}) (8 x^{2} - 16 x + 16)

\frac{d}{d x} (8 x^{2} - 16 x + 16) = 16 x - 16

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

= (16 x - 16) e^{x} + e^{x} (8 x^{2} - 16 x + 16)

Simplify

(16 x - 16) e^{x} + e^{x} (8 x^{2} - 16 x + 16) : 8 e^{x} x^{2}

= 8 e^{x} x^{2}

Popular Examples

derivative of (4x/(x+1))

\frac{d}{d x} (\frac{4 x}{x + 1})

(\partial)/(\partial y)(e^{y/x})

\frac{\partial}{\partial y} (e^{\frac{y}{x}})

integral of xsqrt((8-5x^2)^3)

\int x (8 - 5 x^{2})^{3} d x

derivative of x^3-sqrt(x)derivative of

x^{3} - x

(\partial)/(\partial x)((3x)/(y^2))

\frac{\partial}{\partial x} (\frac{3 x}{y ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of y=(8x^2-16x+16)e^x ?
The derivative of y=(8x^2-16x+16)e^x is 8e^xx^2
What is the first derivative of y=(8x^2-16x+16)e^x ?
The first derivative of y=(8x^2-16x+16)e^x is 8e^xx^2