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Popular >

derivative of (6x^2-12x+12e^x)

Solution

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})

Solution

6 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})

Apply the Product Rule:

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

f = 6 x^{2} - 12 x + 12, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 12 x + 12) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 12 x + 12)

\frac{d}{d x} (6 x^{2} - 12 x + 12) = 12 x - 12

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

= (12 x - 12) e^{x} + e^{x} (6 x^{2} - 12 x + 12)

Simplify

(12 x - 12) e^{x} + e^{x} (6 x^{2} - 12 x + 12) : 6 e^{x} x^{2}

= 6 e^{x} x^{2}

Popular Examples

derivative of (6x^2+4x+4)/(sqrt(x))derivative of

\frac{6 x ^{2} + 4 x + 4}{x}

integral of (x^2+2x+1)^5(x+1)

\int (x^{2} + 2 x + 1)^{5} (x + 1) d x

integral from-1 to 4 of 4-x^2+3x

\int_{- 1}^{4} 4 - x^{2} + 3 x d x

integral of (1/3)x^3

\int (\frac{1}{3}) x^{3} d x

limit as x approaches 1 of (x+1)/(x-1)

x \to 1 lim (\frac{x + 1}{x - 1})

Frequently Asked Questions (FAQ)

What is the derivative of (6x^2-12x+12e^x) ?
The derivative of (6x^2-12x+12e^x) is 6e^xx^2
What is the first derivative of (6x^2-12x+12e^x) ?
The first derivative of (6x^2-12x+12e^x) is 6e^xx^2