What is the derivative of 0.5x^2e^{-0.6x} ?

The derivative of 0.5x^2e^{-0.6x} is 0.5(2e^{-0.6x}x-0.6e^{-0.6x}x^2)

What is the first derivative of 0.5x^2e^{-0.6x} ?

The first derivative of 0.5x^2e^{-0.6x} is 0.5(2e^{-0.6x}x-0.6e^{-0.6x}x^2)

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\frac{d}{d x} (0.5 x^{2} e^{- 0.6 x})

0.5 (2 e^{- 0.6 x} x - 0.6 e^{- 0.6 x} x^{2})

Solution steps

\frac{d}{d x} (0.5 x^{2} e^{- 0.6 x})

Take the constant out:

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

= 0.5 \frac{d}{d x} (x^{2} e^{- 0.6 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 0.6 x}

= 0.5 (\frac{d}{d x} (x^{2}) e^{- 0.6 x} + \frac{d}{d x} (e^{- 0.6 x}) x^{2})

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

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

= 0.5 (2 x e^{- 0.6 x} + (- 0.6 e^{- 0.6 x}) x^{2})

Simplify

= 0.5 (2 e^{- 0.6 x} x - 0.6 e^{- 0.6 x} x^{2})

x ln (x) y^{^{'}} + y = 8 x e^{x}

\frac{x}{1 - x ^{2}}

n = 0 \sum \infty \frac{1}{n ln ( n )}

\frac{\partial}{\partial x} (x^{2} y + 2 y^{2} - 4 x y + 6)

\int \frac{y ^{2} + 20 y + 100}{( y ^{2} + 100 ) ^{2}} d y

What is the derivative of 0.5x^2e^{-0.6x} ?
The derivative of 0.5x^2e^{-0.6x} is 0.5(2e^{-0.6x}x-0.6e^{-0.6x}x^2)
What is the first derivative of 0.5x^2e^{-0.6x} ?
The first derivative of 0.5x^2e^{-0.6x} is 0.5(2e^{-0.6x}x-0.6e^{-0.6x}x^2)