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

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

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

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

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derivative of

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

5 e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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