What is the derivative of 9xe^{-kx} ?

The derivative of 9xe^{-kx} is 9(e^{-xk}-e^{-xk}xk)

What is the first derivative of 9xe^{-kx} ?

The first derivative of 9xe^{-kx} is 9(e^{-xk}-e^{-xk}xk)

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derivative of

9 x e^{- k x}

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

Solution steps

\frac{d}{d x} (9 x e^{- k x})

Treat

k

as a constant

Take the constant out:

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

= 9 \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}

= 9 (\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}

= 9 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 9 (e^{- x k} - e^{- x k} x k)

y = 4 - x^{2}, y = 14 - 7 x

\int 8 cos (x) + 3 x - 8 d x

y = ln (\frac{1}{( x - 2 ) ^{3}})

- 5 e^{4 t}

\frac{\partial}{\partial x} (x sin (2 x^{2} y))

What is the derivative of 9xe^{-kx} ?
The derivative of 9xe^{-kx} is 9(e^{-xk}-e^{-xk}xk)
What is the first derivative of 9xe^{-kx} ?
The first derivative of 9xe^{-kx} is 9(e^{-xk}-e^{-xk}xk)