What is the derivative of (t(t-2)e^t) ?

The derivative of (t(t-2)e^t) is e^xx^2-2e^x

What is the first derivative of (t(t-2)e^t) ?

The first derivative of (t(t-2)e^t) is e^xx^2-2e^x

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

e^{x} x^{2} - 2 e^{x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 2) e^{x}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x - 2) e^{x} + (e^{x} x - e^{x}) x

Simplify

1 \cdot (x - 2) e^{x} + (e^{x} x - e^{x}) x : e^{x} x^{2} - 2 e^{x}

= e^{x} x^{2} - 2 e^{x}

\frac{5 ( x + 20 )}{2}

d (3 e^{x} + 1)

sec (a) n t e (90 - θ) - sin (o) (90 - θ)

ln (x^{3} + 5)

(6 x - y^{2}) d x

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