What is the derivative of 6xe^{-kx} ?

The derivative of 6xe^{-kx} is 6(e^{-kx}-ke^{-kx}x)

What is the first derivative of 6xe^{-kx} ?

The first derivative of 6xe^{-kx} is 6(e^{-kx}-ke^{-kx}x)

Popular >

\frac{d}{d x} (6 x e^{- k x})

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

Solution steps

\frac{d}{d x} (6 x e^{- k x})

Take the constant out:

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

= 6 \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}

= 6 (\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}

= 6 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 6 (e^{- k x} - k e^{- k x} x)

- 5 e^{- x} + 30 e^{- 5 x}

\int \frac{1 - 3 t}{t ^{2}} d t

f (x) = \frac{4 x ^{2} - 7 x + 5}{2 x + 3}

f (x) = 15 e^{x^{2}}

f (x) = 3 x^{2} + 12

What is the derivative of 6xe^{-kx} ?
The derivative of 6xe^{-kx} is 6(e^{-kx}-ke^{-kx}x)
What is the first derivative of 6xe^{-kx} ?
The first derivative of 6xe^{-kx} is 6(e^{-kx}-ke^{-kx}x)