What is the derivative of f(x)=x^2e^{-7x} ?

The derivative of f(x)=x^2e^{-7x} is 2e^{-7x}x-7e^{-7x}x^2

What is the first derivative of f(x)=x^2e^{-7x} ?

The first derivative of f(x)=x^2e^{-7x} is 2e^{-7x}x-7e^{-7x}x^2

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derivative of

f (x) = x^{2} e^{- 7 x}

2 e^{- 7 x} x - 7 e^{- 7 x} x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{- 7 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 7 x}

= \frac{d}{d x} (x^{2}) e^{- 7 x} + \frac{d}{d x} (e^{- 7 x}) x^{2}

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

\frac{d}{d x} (e^{- 7 x}) = - 7 e^{- 7 x}

= 2 x e^{- 7 x} + (- 7 e^{- 7 x}) x^{2}

Simplify

= 2 e^{- 7 x} x - 7 e^{- 7 x} x^{2}

What is the derivative of f(x)=x^2e^{-7x} ?
The derivative of f(x)=x^2e^{-7x} is 2e^{-7x}x-7e^{-7x}x^2
What is the first derivative of f(x)=x^2e^{-7x} ?
The first derivative of f(x)=x^2e^{-7x} is 2e^{-7x}x-7e^{-7x}x^2