What is the derivative of f(x)=(x+3)^2e^{-x} ?

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

What is the first derivative of f(x)=(x+3)^2e^{-x} ?

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = (x + 3)^{2}, g = e^{- x}

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

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

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

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

Simplify

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

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

4 x^{2} ln (4 x)

\frac{\partial}{\partial x} (- x^{3} y^{2})

\int sin^{3} (20 x) d x

x \to 0 + lim (x^{14 x})

\frac{d}{d t} (- 12 cos^{2} (t) sin (t))

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