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Popular >

derivative of (12x^2-24x+24)e^x

Solution

derivative of

(12 x^{2} - 24 x + 24) e^{x}

Solution

12 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((12 x^{2} - 24 x + 24) e^{x})

Apply the Product Rule:

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

f = 12 x^{2} - 24 x + 24, g = e^{x}

= \frac{d}{d x} (12 x^{2} - 24 x + 24) e^{x} + \frac{d}{d x} (e^{x}) (12 x^{2} - 24 x + 24)

\frac{d}{d x} (12 x^{2} - 24 x + 24) = 24 x - 24

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

= (24 x - 24) e^{x} + e^{x} (12 x^{2} - 24 x + 24)

Simplify

(24 x - 24) e^{x} + e^{x} (12 x^{2} - 24 x + 24) : 12 e^{x} x^{2}

= 12 e^{x} x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of (12x^2-24x+24)e^x ?
The derivative of (12x^2-24x+24)e^x is 12e^xx^2
What is the first derivative of (12x^2-24x+24)e^x ?
The first derivative of (12x^2-24x+24)e^x is 12e^xx^2