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Popular >

derivative of x^3*e^{-x}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= 3 e^{- x} x^{2} - e^{- x} x^{3}

Popular Examples

derivative of x^4-8x^3+22x^2-24x+9

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

tangent of x^4+xy^2=5,(1,2)tangent of

x^{4} + x y^{2} = 5, (1, 2)

derivative of 4x-2/(x^3)

\frac{d}{d x} (4 x - \frac{2}{x ^{3}})

(\partial)/(\partial x)(x/(x+y)+e^{xy}x+4y)

\frac{\partial}{\partial x} (\frac{x}{x + y} + e^{x y} x + 4 y)

derivative of (x-x^2/(sqrt(x)))

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

Frequently Asked Questions (FAQ)

What is the derivative of x^3*e^{-x} ?
The derivative of x^3*e^{-x} is 3e^{-x}x^2-e^{-x}x^3
What is the first derivative of x^3*e^{-x} ?
The first derivative of x^3*e^{-x} is 3e^{-x}x^2-e^{-x}x^3