What is the derivative of (2x-3)e^{2-x} ?

The derivative of (2x-3)e^{2-x} is -2e^{-x+2}x+5e^{-x+2}

What is the first derivative of (2x-3)e^{2-x} ?

The first derivative of (2x-3)e^{2-x} is -2e^{-x+2}x+5e^{-x+2}

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derivative of

(2 x - 3) e^{2 - x}

- 2 e^{- x + 2} x + 5 e^{- x + 2}

Solution steps

\frac{d}{d x} ((2 x - 3) e^{2 - x})

Apply the Product Rule:

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

f = 2 x - 3, g = e^{2 - x}

= \frac{d}{d x} (2 x - 3) e^{2 - x} + \frac{d}{d x} (e^{2 - x}) (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

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

= 2 e^{2 - x} + (- e^{2 - x}) (2 x - 3)

Simplify

2 e^{2 - x} + (- e^{2 - x}) (2 x - 3) : - 2 e^{- x + 2} x + 5 e^{- x + 2}

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

\frac{d}{d x} (x^{2} + 2 y^{2})

\frac{d}{d x} (x^{3} - 3 x^{2} + 2)

y = x^{2} - 2, (- 3, 7)

3 x y^{^{'}} = y^{2} - y - 2

f (x) = ln (3 x)

What is the derivative of (2x-3)e^{2-x} ?
The derivative of (2x-3)e^{2-x} is -2e^{-x+2}x+5e^{-x+2}
What is the first derivative of (2x-3)e^{2-x} ?
The first derivative of (2x-3)e^{2-x} is -2e^{-x+2}x+5e^{-x+2}