What is the derivative of f(x)=x^3+4e^{-0.5x} ?

The derivative of f(x)=x^3+4e^{-0.5x} is 3x^2-2e^{-0.5x}

What is the first derivative of f(x)=x^3+4e^{-0.5x} ?

The first derivative of f(x)=x^3+4e^{-0.5x} is 3x^2-2e^{-0.5x}

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derivative of

f (x) = x^{3} + 4 e^{- 0.5 x}

3 x^{2} - 2 e^{- 0.5 x}

Solution steps

\frac{d}{d x} (x^{3} + 4 e^{- 0.5 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (4 e^{- 0.5 x})

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

\frac{d}{d x} (4 e^{- 0.5 x}) = - 2 e^{- 0.5 x}

= 3 x^{2} - 2 e^{- 0.5 x}

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What is the derivative of f(x)=x^3+4e^{-0.5x} ?
The derivative of f(x)=x^3+4e^{-0.5x} is 3x^2-2e^{-0.5x}
What is the first derivative of f(x)=x^3+4e^{-0.5x} ?
The first derivative of f(x)=x^3+4e^{-0.5x} is 3x^2-2e^{-0.5x}