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}

\int cos (x) (8 + 7 sin^{2} (x)) d x

\int e^{- 20 x} d x

y = 10 x sin (x)

\frac{d}{d x} (9 x (- 2)^{2} - 3 x (- 2) - 1)

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}