What is the derivative of 2x^3e^{-0.6x} ?

The derivative of 2x^3e^{-0.6x} is 2(3e^{-0.6x}x^2-0.6e^{-0.6x}x^3)

What is the first derivative of 2x^3e^{-0.6x} ?

The first derivative of 2x^3e^{-0.6x} is 2(3e^{-0.6x}x^2-0.6e^{-0.6x}x^3)

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\frac{d}{d x} (2 x^{3} e^{- 0.6 x})

2 (3 e^{- 0.6 x} x^{2} - 0.6 e^{- 0.6 x} x^{3})

Solution steps

\frac{d}{d x} (2 x^{3} e^{- 0.6 x})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{3} e^{- 0.6 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{- 0.6 x}

= 2 (\frac{d}{d x} (x^{3}) e^{- 0.6 x} + \frac{d}{d x} (e^{- 0.6 x}) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{- 0.6 x}) = - 0.6 e^{- 0.6 x}

= 2 (3 x^{2} e^{- 0.6 x} + (- 0.6 e^{- 0.6 x}) x^{3})

Simplify

= 2 (3 e^{- 0.6 x} x^{2} - 0.6 e^{- 0.6 x} x^{3})

\int \frac{v}{v ^{2} + 1} d v

\int \frac{x ^{2} + 6}{x ^{3} + x ^{2} - 2 x} d x

f (x) = \frac{2}{x + 7}, (- 8, - 2)

\frac{d}{d x} (e^{x} arctan (x))

x (\frac{d y}{d x}) = \frac{1}{y ^{3}}

What is the derivative of 2x^3e^{-0.6x} ?
The derivative of 2x^3e^{-0.6x} is 2(3e^{-0.6x}x^2-0.6e^{-0.6x}x^3)
What is the first derivative of 2x^3e^{-0.6x} ?
The first derivative of 2x^3e^{-0.6x} is 2(3e^{-0.6x}x^2-0.6e^{-0.6x}x^3)