What is the derivative of e^{-x}x^2+3e^{-x}-e^{-x} ?

The derivative of e^{-x}x^2+3e^{-x}-e^{-x} is -e^{-x}x^2+2e^{-x}x-2e^{-x}

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

The first derivative of e^{-x}x^2+3e^{-x}-e^{-x} is -e^{-x}x^2+2e^{-x}x-2e^{-x}

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derivative of

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

- e^{- x} x^{2} + 2 e^{- x} x - 2 e^{- x}

Solution steps

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

Simplify

e^{- x} x^{2} + 3 e^{- x} - e^{- x} : e^{- x} x^{2} + 2 e^{- x}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

x y^{^{'}} + y + x = 0, y (1) = 1

\frac{\partial}{\partial x} (ln (x^{5} - y^{4}))

\frac{d}{d x} (a cos (3 x))

(3 x^{2})^{2 x}

\int \frac{1}{4} x^{- \frac{3}{4}} d x

What is the derivative of e^{-x}x^2+3e^{-x}-e^{-x} ?
The derivative of e^{-x}x^2+3e^{-x}-e^{-x} is -e^{-x}x^2+2e^{-x}x-2e^{-x}
What is the first derivative of e^{-x}x^2+3e^{-x}-e^{-x} ?
The first derivative of e^{-x}x^2+3e^{-x}-e^{-x} is -e^{-x}x^2+2e^{-x}x-2e^{-x}