What is (\partial)/(\partial x)(x^{1/2}+y^{1/3}) ?

The answer to (\partial)/(\partial x)(x^{1/2}+y^{1/3}) is 1/(2x^{1/2)}

(\partial)/(\partial x)(x^{1/2}+y^{1/3})

\frac{\partial}{\partial x} (x^{\frac{1}{2}} + y^{\frac{1}{3}})

\frac{1}{2 x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{2}} + y^{\frac{1}{3}})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{\frac{1}{2}}) + \frac{\partial}{\partial x} (y^{\frac{1}{3}})

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

\frac{\partial}{\partial x} (y^{\frac{1}{3}}) = 0

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

Simplify

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

\int_{81}^{v} \frac{1}{v} d v

\int (25 - x^{2}) d x

d er i v a t i v e x^{2} sin^{7} (x) + x cos^{- 3} (x)

\int 0.2 x + 8 d x

e^{x}, e^{- x}, x = - 2, x = 1

What is (\partial)/(\partial x)(x^{1/2}+y^{1/3}) ?
The answer to (\partial)/(\partial x)(x^{1/2}+y^{1/3}) is 1/(2x^{1/2)}