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Popular >

derivative of ax^2e^{-5x}

Solution

\frac{d}{d x} (a x^{2} e^{- 5 x})

Solution

a (2 e^{- 5 x} x - 5 e^{- 5 x} x^{2})

Solution steps

\frac{d}{d x} (a x^{2} e^{- 5 x})

Take the constant out:

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

= a \frac{d}{d x} (x^{2} e^{- 5 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 5 x}

= a (\frac{d}{d x} (x^{2}) e^{- 5 x} + \frac{d}{d x} (e^{- 5 x}) x^{2})

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

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

= a (2 x e^{- 5 x} + (- 5 e^{- 5 x}) x^{2})

Simplify

= a (2 e^{- 5 x} x - 5 e^{- 5 x} x^{2})

Graph

Popular Examples

integral from-pi to pi of xcos(nx)

\int_{- π}^{π} x cos (n x) d x

integral of (5e^{6/(x^4)})/(x^5)

\int \frac{5 e ^{\frac{6}{x ^{4}}}}{x ^{5}} d x

(\partial)/(\partial y)(y+sin(x/y))

\frac{\partial}{\partial y} (y + sin (\frac{x}{y}))

tangent of y=(|x|)/(sqrt(2-x^2)),(1,1)tangent of

y = \frac{∣ x ∣}{2 - x ^{2}}, (1, 1)

tangent of f(x)=5x^3sin(x)tangent of

f (x) = 5 x^{3} sin (x)

Frequently Asked Questions (FAQ)

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