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Popular >

derivative of x^2e^{-0.04x}

Solution

\frac{d}{d x} (x^{2} e^{- 0.04 x})

Solution

2 e^{- 0.04 x} x - 0.04 e^{- 0.04 x} x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{- 0.04 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 0.04 x}

= \frac{d}{d x} (x^{2}) e^{- 0.04 x} + \frac{d}{d x} (e^{- 0.04 x}) x^{2}

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

\frac{d}{d x} (e^{- 0.04 x}) = - 0.04 e^{- 0.04 x}

= 2 x e^{- 0.04 x} + (- 0.04 e^{- 0.04 x}) x^{2}

Simplify

= 2 e^{- 0.04 x} x - 0.04 e^{- 0.04 x} x^{2}

Popular Examples

(\partial)/(\partial y)(xe^{-2x})

\frac{\partial}{\partial y} (x e^{- 2 x})

(\partial)/(\partial x)(xy^2z)

\frac{\partial}{\partial x} (x y^{2} z)

integral of (3-x)^3

\int (3 - x)^{3} d x

normal of y=x^4+8e^x,(0,8)normal of

y = x^{4} + 8 e^{x}, (0, 8)

integral of cos(2x+3)

\int cos (2 x + 3) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2e^{-0.04x} ?
The derivative of x^2e^{-0.04x} is 2e^{-0.04x}x-0.04e^{-0.04x}x^2
What is the first derivative of x^2e^{-0.04x} ?
The first derivative of x^2e^{-0.04x} is 2e^{-0.04x}x-0.04e^{-0.04x}x^2