What is the derivative of (10x^2-20x+20)e^x ?

The derivative of (10x^2-20x+20)e^x is 10e^xx^2

What is the first derivative of (10x^2-20x+20)e^x ?

The first derivative of (10x^2-20x+20)e^x is 10e^xx^2

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derivative of

(10 x^{2} - 20 x + 20) e^{x}

10 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((10 x^{2} - 20 x + 20) e^{x})

Apply the Product Rule:

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

f = 10 x^{2} - 20 x + 20, g = e^{x}

= \frac{d}{d x} (10 x^{2} - 20 x + 20) e^{x} + \frac{d}{d x} (e^{x}) (10 x^{2} - 20 x + 20)

\frac{d}{d x} (10 x^{2} - 20 x + 20) = 20 x - 20

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

= (20 x - 20) e^{x} + e^{x} (10 x^{2} - 20 x + 20)

Simplify

(20 x - 20) e^{x} + e^{x} (10 x^{2} - 20 x + 20) : 10 e^{x} x^{2}

= 10 e^{x} x^{2}

y = 4 e^{2 x}

\int_{0}^{4} 0.125 x d x

n = 1 \sum \infty 6 e^{- 2 n}

\int 5 e^{2 - x} d x

f (θ) = 2 θ

What is the derivative of (10x^2-20x+20)e^x ?
The derivative of (10x^2-20x+20)e^x is 10e^xx^2
What is the first derivative of (10x^2-20x+20)e^x ?
The first derivative of (10x^2-20x+20)e^x is 10e^xx^2