What is the derivative of f(x)=e^x(3x^2-6x+6) ?

The derivative of f(x)=e^x(3x^2-6x+6) is 3e^xx^2

What is the first derivative of f(x)=e^x(3x^2-6x+6) ?

The first derivative of f(x)=e^x(3x^2-6x+6) is 3e^xx^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

3 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = 3 x^{2} - 6 x + 6

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

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

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

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

Simplify

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

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

y^{^{'}} = (t + y)^{2} - 1, y (1) = 5

\frac{d}{d x} (\frac{2}{x ^{2} - 4})

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

\int_{- 2}^{3} x d x

\int_{0}^{2} (x^{2} - 3 x) d x

What is the derivative of f(x)=e^x(3x^2-6x+6) ?
The derivative of f(x)=e^x(3x^2-6x+6) is 3e^xx^2
What is the first derivative of f(x)=e^x(3x^2-6x+6) ?
The first derivative of f(x)=e^x(3x^2-6x+6) is 3e^xx^2