What is (\partial)/(\partial x)(sqrt(2x+1)+ye^{-x}) ?

The answer to (\partial)/(\partial x)(sqrt(2x+1)+ye^{-x}) is 1/(sqrt(2x+1))-ye^{-x}

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(\partial)/(\partial x)(sqrt(2x+1)+ye^{-x})

\frac{\partial}{\partial x} (2 x + 1 + y e^{- x})

\frac{1}{2 x + 1} - y e^{- x}

Solution steps

\frac{\partial}{\partial x} (2 x + 1 + y e^{- x})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x + 1) + \frac{\partial}{\partial x} (y e^{- x})

\frac{\partial}{\partial x} (2 x + 1) = \frac{1}{2 x + 1}

\frac{\partial}{\partial x} (y e^{- x}) = - y e^{- x}

= \frac{1}{2 x + 1} - y e^{- x}

What is (\partial)/(\partial x)(sqrt(2x+1)+ye^{-x}) ?
The answer to (\partial)/(\partial x)(sqrt(2x+1)+ye^{-x}) is 1/(sqrt(2x+1))-ye^{-x}