What is the derivative of e^x(5x^2-10x+10) ?

The derivative of e^x(5x^2-10x+10) is 5e^xx^2

What is the first derivative of e^x(5x^2-10x+10) ?

The first derivative of e^x(5x^2-10x+10) is 5e^xx^2

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derivative of

e^{x} (5 x^{2} - 10 x + 10)

5 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (5 x^{2} - 10 x + 10))

Apply the Product Rule:

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

f = e^{x}, g = 5 x^{2} - 10 x + 10

= \frac{d}{d x} (e^{x}) (5 x^{2} - 10 x + 10) + \frac{d}{d x} (5 x^{2} - 10 x + 10) e^{x}

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

\frac{d}{d x} (5 x^{2} - 10 x + 10) = 10 x - 10

= e^{x} (5 x^{2} - 10 x + 10) + (10 x - 10) e^{x}

Simplify

e^{x} (5 x^{2} - 10 x + 10) + (10 x - 10) e^{x} : 5 e^{x} x^{2}

= 5 e^{x} x^{2}

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What is the derivative of e^x(5x^2-10x+10) ?
The derivative of e^x(5x^2-10x+10) is 5e^xx^2
What is the first derivative of e^x(5x^2-10x+10) ?
The first derivative of e^x(5x^2-10x+10) is 5e^xx^2