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Popular >

derivative of Ax^2e^{-x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of ((arcsin(1-x-1+x))/2)

\frac{d}{d x} (\frac{( arcsin ( 1 - x ) - 1 + x )}{2})

(\partial)/(\partial x)(1/4 x^3)

\frac{\partial}{\partial x} (\frac{1}{4} x^{3})

integral of 1/(sqrt(16x^2-81))

\int \frac{1}{16 x ^{2} - 81} d x

integral of ln(3/x)

\int ln (\frac{3}{x}) d x

integral of-2/((x+1)^2)

\int - \frac{2}{( x + 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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