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Popular >

derivative of Axe^{(-bx})

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of 1/(x^2+9x+20)

\int \frac{1}{x ^{2} + 9 x + 20} d x

integral of (csc^2(x))/(1+cot(x))

\int \frac{csc ^{2} ( x )}{1 + cot ( x )} d x

y^{''}-2y^'+2y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

derivative of x^{sqrt(2)e^{-42}}derivative of

x^{2 e^{- 42}}

area 9/x ,2x, 1/2 x area

\frac{9}{x}, 2 x, \frac{1}{2} x

Frequently Asked Questions (FAQ)

What is the derivative of Axe^{(-bx}) ?
The derivative of Axe^{(-bx}) is A(e^{-bx}-be^{-bx}x)
What is the first derivative of Axe^{(-bx}) ?
The first derivative of Axe^{(-bx}) is A(e^{-bx}-be^{-bx}x)