What is the derivative of 5xe^{-kx} ?

The derivative of 5xe^{-kx} is 5(e^{-xk}-e^{-xk}xk)

What is the first derivative of 5xe^{-kx} ?

The first derivative of 5xe^{-kx} is 5(e^{-xk}-e^{-xk}xk)

Popular >

derivative of

5 x e^{- k x}

5 (e^{- x k} - e^{- x k} x k)

Solution steps

\frac{d}{d x} (5 x e^{- k x})

Treat

k

as a constant

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{- k x})

Apply the Product Rule:

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

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

= 5 (\frac{d x}{d x} e^{- k x} + \frac{d}{d x} (e^{- k x}) x)

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

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

= 5 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 5 (e^{- x k} - e^{- x k} x k)

\frac{d}{d x} (arcsin (x^{2} - 4))

y = e^{- 2 ((x - 146) - 2 (\frac{l n ( 19.52 )}{2}))}

\int_{0}^{3} (x - 1) d x

\int (3 x^{2} - 7 x + 4) d x

\int \frac{3 x ^{3} 9 x ^{2} - 15}{x ^{2} 4 x ^{4}} d x

What is the derivative of 5xe^{-kx} ?
The derivative of 5xe^{-kx} is 5(e^{-xk}-e^{-xk}xk)
What is the first derivative of 5xe^{-kx} ?
The first derivative of 5xe^{-kx} is 5(e^{-xk}-e^{-xk}xk)