What is the derivative of 8xe^{-kx} ?

The derivative of 8xe^{-kx} is 8(e^{-xk}-e^{-xk}xk)

What is the first derivative of 8xe^{-kx} ?

The first derivative of 8xe^{-kx} is 8(e^{-xk}-e^{-xk}xk)

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derivative of

8 x e^{- k x}

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

Solution steps

\frac{d}{d x} (8 x e^{- k x})

Treat

k

as a constant

Take the constant out:

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

= 8 \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}

= 8 (\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}

= 8 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 8 (e^{- x k} - e^{- x k} x k)

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

\frac{d}{d x} (x^{2} + 9 x)

\frac{\partial}{\partial x} (e^{x^{2} - y^{2}} (cos (2 x y) + sin (2 x y)))

4 x - 3 x^{2}

- 30 t^{2} + 380 t, 7, 14

What is the derivative of 8xe^{-kx} ?
The derivative of 8xe^{-kx} is 8(e^{-xk}-e^{-xk}xk)
What is the first derivative of 8xe^{-kx} ?
The first derivative of 8xe^{-kx} is 8(e^{-xk}-e^{-xk}xk)