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Popular >

derivative of (ax+be^{-x})

Solution

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

Solution

a e^{- x} - e^{- x} (a x + b)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (a x + b) = a

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

= a e^{- x} + (- e^{- x}) (a x + b)

Simplify

= a e^{- x} - e^{- x} (a x + b)

Popular Examples

integral of [sqrt(x)(x^2-1)+csc^2(x)]

\int [x (x^{2} - 1) + csc^{2} (x)] d x

derivative of 4sin(x)sin(x)derivative of

4 sin (x) sin (x)

inverse oflaplace (s+5)/(s^2+5s+9)inverse laplace

\frac{s + 5}{s ^{2} + 5 s + 9}

y^{''}+4y=t^2+3e^t,y(0)=0,y^'(0)=2

y^{^{''}} + 4 y = t^{2} + 3 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

integral of y^3

\int y^{3} d y

Frequently Asked Questions (FAQ)

What is the derivative of (ax+be^{-x}) ?
The derivative of (ax+be^{-x}) is ae^{-x}-e^{-x}(ax+b)
What is the first derivative of (ax+be^{-x}) ?
The first derivative of (ax+be^{-x}) is ae^{-x}-e^{-x}(ax+b)