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

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

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

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

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derivative of

3 x e^{- x}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

\int - 2 x + 9 x^{2} - 4 x^{3} + 16 d x

\int e^{7 x} sin (3 x) d x

\int 8 tan^{3} (x) sec (x) d x

\frac{d}{d x} (3 x^{2} - 10)

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