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

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

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

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

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derivative of

y = 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})

f (x) = 2^{20}

f (x) = 2 - x

\frac{d}{d x} (\frac{( 3 x ^{2} - 5 ) ^{4}}{( 4 x ^{3} + 2 ) ^{5}})

y = - x^{2} + 4 x

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

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