What is (\partial)/(\partial y)(x+2y^{1/2}) ?

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

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(\partial)/(\partial y)(x+2y^{1/2})

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

\frac{1}{y ^{\frac{1}{2}}}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x) = 0

\frac{\partial}{\partial y} (2 y^{\frac{1}{2}}) = \frac{1}{y ^{\frac{1}{2}}}

= 0 + \frac{1}{y ^{\frac{1}{2}}}

Simplify

= \frac{1}{y ^{\frac{1}{2}}}

y = \frac{7}{x - 1}

4 cos (5 ln (x))

(cos (t) + t sin (t)) + (sin (t) - t cos (t))

\int 9 x^{4} cos (x^{5} + 6) d x

\frac{\partial}{\partial x} (a sin (x) cos (y))

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