What is the derivative of y=4x^3e^{-x} ?

The derivative of y=4x^3e^{-x} is 4(3e^{-x}x^2-e^{-x}x^3)

What is the first derivative of y=4x^3e^{-x} ?

The first derivative of y=4x^3e^{-x} is 4(3e^{-x}x^2-e^{-x}x^3)

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derivative of

y = 4 x^{3} e^{- x}

4 (3 e^{- x} x^{2} - e^{- x} x^{3})

Solution steps

\frac{d}{d x} (4 x^{3} e^{- x})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{3} e^{- x})

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (x^{3}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{3})

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

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

= 4 (3 x^{2} e^{- x} + (- e^{- x}) x^{3})

Simplify

= 4 (3 e^{- x} x^{2} - e^{- x} x^{3})

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

f (x) = e^{x}, x = 0

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

f (x) = 5 x^{3}, - 10, 15, at x = 0

\frac{\partial}{\partial x} (1 - x^{2} - y^{2})

What is the derivative of y=4x^3e^{-x} ?
The derivative of y=4x^3e^{-x} is 4(3e^{-x}x^2-e^{-x}x^3)
What is the first derivative of y=4x^3e^{-x} ?
The first derivative of y=4x^3e^{-x} is 4(3e^{-x}x^2-e^{-x}x^3)