What is the d/(dy)(x+3y^{1/3}) ?

The d/(dy)(x+3y^{1/3}) is 1/(y^{2/3)}

What is the first d/(dy)(x+3y^{1/3}) ?

The first d/(dy)(x+3y^{1/3}) is 1/(y^{2/3)}

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

\frac{1}{y ^{\frac{2}{3}}}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d y} = 0

\frac{d}{d y} (3 y^{\frac{1}{3}}) = \frac{1}{y ^{\frac{2}{3}}}

= 0 + \frac{1}{y ^{\frac{2}{3}}}

Simplify

= \frac{1}{y ^{\frac{2}{3}}}

What is the d/(dy)(x+3y^{1/3}) ?
The d/(dy)(x+3y^{1/3}) is 1/(y^{2/3)}
What is the first d/(dy)(x+3y^{1/3}) ?
The first d/(dy)(x+3y^{1/3}) is 1/(y^{2/3)}