What is the derivative of y=4xe^{-kx} ?

The derivative of y=4xe^{-kx} is 4(e^{-kx}-ke^{-kx}x)

What is the first derivative of y=4xe^{-kx} ?

The first derivative of y=4xe^{-kx} is 4(e^{-kx}-ke^{-kx}x)

Popular >

derivative of

y = 4 x e^{- k x}

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

Solution steps

\frac{d}{d x} (4 x e^{- k x})

Take the constant out:

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

= 4 \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}

= 4 (\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}

= 4 (1 \cdot e^{- k x} + (- k e^{- k x}) x)

Simplify

= 4 (e^{- k x} - k e^{- k x} x)

\int \frac{64 - x ^{2}}{x} d x

f (x) = 2 x^{2} - 3 x, at x = 2

\frac{d}{d x} (x^{3} - 3 x + 5)

n = 1 \sum \infty e^{- \frac{3}{n ^{2}}}

\int_{1}^{\infty} \frac{3}{x ^{2} + 1} d x

What is the derivative of y=4xe^{-kx} ?
The derivative of y=4xe^{-kx} is 4(e^{-kx}-ke^{-kx}x)
What is the first derivative of y=4xe^{-kx} ?
The first derivative of y=4xe^{-kx} is 4(e^{-kx}-ke^{-kx}x)