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Popular >

derivative of (Ax+Be^{-x})

Solution

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

Solution

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

Solution steps

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

Treat

A, B

as constants

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

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

Popular Examples

sum from n=1 to infinity of 1/(n(2n-1))

n = 1 \sum \infty \frac{1}{n ( 2 n - 1 )}

tangent of f(x)= 1/(sqrt(8x))tangent of

f (x) = \frac{1}{8 x}

derivative of (x+1^{-1})

\frac{d}{d x} ((x + 1)^{- 1})

integral of (2x+2y)

\int (2 x + 2 y) d y

derivative of ln((7x+8/(4x+8)))

\frac{d}{d x} (ln (\frac{7 x + 8}{4 x + 8}))

Frequently Asked Questions (FAQ)

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