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Popular >

derivative of (Ax^2+Bxe^{-x})

Solution

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

Solution

e^{- x} (2 A x + B) - e^{- x} (A x^{2} + x B)

Solution steps

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

Treat

A, B

as constants

Apply the Product Rule:

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

f = A x^{2} + B x, g = e^{- x}

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

\frac{d}{d x} (A x^{2} + B x) = 2 A x + B

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

= (2 A x + B) e^{- x} + (- e^{- x}) (A x^{2} + B x)

Simplify

= e^{- x} (2 A x + B) - e^{- x} (A x^{2} + x B)

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Frequently Asked Questions (FAQ)

What is the derivative of (Ax^2+Bxe^{-x}) ?
The derivative of (Ax^2+Bxe^{-x}) is e^{-x}(2Ax+B)-e^{-x}(Ax^2+xB)
What is the first derivative of (Ax^2+Bxe^{-x}) ?
The first derivative of (Ax^2+Bxe^{-x}) is e^{-x}(2Ax+B)-e^{-x}(Ax^2+xB)