What is the derivative of 7xe^{-kx} ?

The derivative of 7xe^{-kx} is 7(e^{-xk}-e^{-xk}xk)

What is the first derivative of 7xe^{-kx} ?

The first derivative of 7xe^{-kx} is 7(e^{-xk}-e^{-xk}xk)

derivative of

7 x e^{- k x}

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

Solution steps

\frac{d}{d x} (7 x e^{- k x})

Treat

k

as a constant

Take the constant out:

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

= 7 \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}

= 7 (\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}

= 7 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 7 (e^{- x k} - e^{- x k} x k)

\int \frac{54}{1 + 36 x ^{2}} d x

f (x) = arcsin (\frac{x}{2})

x \to 0 + lim (ln (x) + \frac{1}{x ^{2}})

\int 2 (x - 2) ln (x - 2) d x

n = 0 \sum \infty \frac{1}{4 n ^{2} - 1}

What is the derivative of 7xe^{-kx} ?
The derivative of 7xe^{-kx} is 7(e^{-xk}-e^{-xk}xk)
What is the first derivative of 7xe^{-kx} ?
The first derivative of 7xe^{-kx} is 7(e^{-xk}-e^{-xk}xk)