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

The derivative of 3xe^{-ax} is 3(e^{-ax}-ae^{-ax}x)

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

The first derivative of 3xe^{-ax} is 3(e^{-ax}-ae^{-ax}x)

Popular >

derivative of

3 x e^{- a x}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- a x}

= 3 (\frac{d x}{d x} e^{- a x} + \frac{d}{d x} (e^{- a x}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- a x}) = - a e^{- a x}

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

Simplify

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

5 t^{2} y^{^{''}} + t y^{^{'}} - 12 y = 0

\int \frac{x ^{2}}{x ^{6} - 9} d x

(3, 0), (6, 2)

\frac{\partial}{\partial z} (\frac{1}{x ^{2} + y ^{2} + z ^{2}})

e^{x^{2}}

What is the derivative of 3xe^{-ax} ?
The derivative of 3xe^{-ax} is 3(e^{-ax}-ae^{-ax}x)
What is the first derivative of 3xe^{-ax} ?
The first derivative of 3xe^{-ax} is 3(e^{-ax}-ae^{-ax}x)