What is the derivative of 3xe^{-kx} ?

The derivative of 3xe^{-kx} is 3(e^{-xk}-e^{-xk}xk)

What is the first derivative of 3xe^{-kx} ?

The first derivative of 3xe^{-kx} is 3(e^{-xk}-e^{-xk}xk)

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derivative of

3 x e^{- k x}

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

Solution steps

\frac{d}{d x} (3 x e^{- k x})

Treat

k

as a constant

Take the constant out:

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

= 3 \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}

= 3 (\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}

= 3 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 3 (e^{- x k} - e^{- x k} x k)

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{( 1 + x )})

x \to 6 lim (\frac{x - 6}{x - 6})

\int 4 x - x^{2} d x

P (x) = x (x - 8) (x + 5)

\int_{0}^{2} (\frac{x}{( 3 - x ) ^{2}}) d x

What is the derivative of 3xe^{-kx} ?
The derivative of 3xe^{-kx} is 3(e^{-xk}-e^{-xk}xk)
What is the first derivative of 3xe^{-kx} ?
The first derivative of 3xe^{-kx} is 3(e^{-xk}-e^{-xk}xk)