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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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