What is the derivative of y=x*e^{4-x} ?

The derivative of y=x*e^{4-x} is e^{4-x}-e^{4-x}x

What is the first derivative of y=x*e^{4-x} ?

The first derivative of y=x*e^{4-x} is e^{4-x}-e^{4-x}x

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derivative of

y = x \cdot e^{4 - x}

e^{4 - x} - e^{4 - x} x

Solution steps

\frac{d}{d x} (x e^{4 - x})

Apply the Product Rule:

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

f = x, g = e^{4 - x}

= \frac{d x}{d x} e^{4 - x} + \frac{d}{d x} (e^{4 - x}) x

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

\frac{d}{d x} (e^{4 - x}) = - e^{4 - x}

= 1 \cdot e^{4 - x} + (- e^{4 - x}) x

Simplify

= e^{4 - x} - e^{4 - x} x

y = x - 1, x - y = 1

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What is the derivative of y=x*e^{4-x} ?
The derivative of y=x*e^{4-x} is e^{4-x}-e^{4-x}x
What is the first derivative of y=x*e^{4-x} ?
The first derivative of y=x*e^{4-x} is e^{4-x}-e^{4-x}x