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

The derivative of x+e^{-2x} is 1-2e^{-2x}

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

The first derivative of x+e^{-2x} is 1-2e^{-2x}

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

1 - 2 e^{- 2 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

= 1 - 2 e^{- 2 x}

x^{2} y d x + (x^{3} + 3 x y^{2}) d y = 0

t y^{^{'}} + (1 + t) y = t

y^{^{''}} + 7 y^{^{'}} + 12 y = 2 e^{t}

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = 4 t^{2}

\int (a + x)^{3} d x

What is the derivative of x+e^{-2x} ?
The derivative of x+e^{-2x} is 1-2e^{-2x}
What is the first derivative of x+e^{-2x} ?
The first derivative of x+e^{-2x} is 1-2e^{-2x}