What is the derivative of 6x^2e^{-x} ?

The derivative of 6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)

What is the first derivative of 6x^2e^{-x} ?

The first derivative of 6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)

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\frac{d}{d x} (6 x^{2} e^{- x})

6 (2 e^{- x} x - e^{- x} x^{2})

Solution steps

\frac{d}{d x} (6 x^{2} e^{- x})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{2} e^{- x})

Apply the Product Rule:

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

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

= 6 (\frac{d}{d x} (x^{2}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{2})

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

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

= 6 (2 x e^{- x} + (- e^{- x}) x^{2})

Simplify

= 6 (2 e^{- x} x - e^{- x} x^{2})

y^{^{''}} + 4 y = 2 e^{x} + sin (2 x)

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

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x)^{2})

\frac{d}{d x} (- x^{3} + 5 x^{2} - 6 x)

\int \frac{( x ^{2} )}{1 + x ^{2}} d x

What is the derivative of 6x^2e^{-x} ?
The derivative of 6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)
What is the first derivative of 6x^2e^{-x} ?
The first derivative of 6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)