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Popular >

derivative of Ae^{-2x}x

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{d x}{d x} = 1

= A ((- 2 e^{- 2 x}) x + 1 \cdot e^{- 2 x})

Simplify

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

Popular Examples

integral of (x^{3/2}+8x+2)

\int (x^{\frac{3}{2}} + 8 x + 2) d x

derivative of 2arctan(3x-ln(2+3x))

\frac{d}{d x} (2 arctan (3 x) - ln (2 + 3 x))

integral from 3 to 6 of 1/(sqrt(36-x^2))

\int_{3}^{6} \frac{1}{36 - x ^{2}} d x

derivative of f(t)=ln(cos(t))derivative of

f (t) = ln (cos (t))

tangent of f(x)=e^xcos(x),(0,1)tangent of

f (x) = e^{x} cos (x), (0, 1)

Frequently Asked Questions (FAQ)

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