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Popular >

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

Solution

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

Solution

12 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (4x-3)/(2x^2-3x-14)

\int \frac{4 x - 3}{2 x ^{2} - 3 x - 14} d x

y^{'''}+8y^{''}+5y^'-50y=0

y^{^{'''}} + 8 y^{^{''}} + 5 y^{^{'}} - 50 y = 0

derivative of ((x+2)/(x-2))^2 derivative of

(\frac{x + 2}{x - 2})^{2}

derivative of e^{xtan(x})

\frac{d}{d x} (e^{x t a n (x)})

tangent of y=x^4+3x^2-x tangent of

y = x^{4} + 3 x^{2} - x

Frequently Asked Questions (FAQ)

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