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

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

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

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

1

Solution steps

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

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

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

= 1 + 0

Simplify

= 1

- y^{^{'}} + \frac{3 y}{x} = \frac{y ^{2}}{x}

\frac{d}{d x} (\frac{7 x ^{2} + 3 x + 7}{x})

x \to 0 + lim (7 (\frac{1}{x} - cot (x)))

y^{^{''}} + 9 y = sec^{2} (3 x)

y = x^{x}

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