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

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

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

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

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

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}

\frac{d}{d x} ((\frac{2}{3})^{x})

f (x) = (4 x - 3) (x + 2)

f (x) = x^{2} + 10

\int sec^{2} (x) tan^{10} (x) d x

e^{(x + 1)}

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