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

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

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}

\int \frac{1}{y ^{2} - y} d y

f (x) = x^{2} + 2

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

x \to 1 lim (\frac{x ^{2} + 7 x}{x})

t^{3}

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