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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of (sec^2(x)-5)

\int (sec^{2} (x) - 5) d x

tangent of f(x)=(1+5x)^9,\at x=0 tangent of

f (x) = (1 + 5 x)^{9}, at x = 0

limit as x approaches 0+of (Inx)/x

x \to 0 + lim (\frac{I n x}{x})

(dy)/(dx)=((xy+3x-y-3))/(xy-2x+4y-8)

\frac{d y}{d x} = \frac{( x y + 3 x - y - 3 )}{x y - 2 x + 4 y - 8}

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

\int \frac{2 x}{x ^{2} + x} d x

Frequently Asked Questions (FAQ)

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