What is (\partial)/(\partial y)(1+x^4+y^3) ?

The answer to (\partial)/(\partial y)(1+x^4+y^3) is 3y^2

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(\partial)/(\partial y)(1+x^4+y^3)

\frac{\partial}{\partial y} (1 + x^{4} + y^{3})

3 y^{2}

Solution steps

\frac{\partial}{\partial y} (1 + x^{4} + y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (1) + \frac{\partial}{\partial y} (x^{4}) + \frac{\partial}{\partial y} (y^{3})

\frac{\partial}{\partial y} (1) = 0

\frac{\partial}{\partial y} (x^{4}) = 0

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

= 0 + 0 + 3 y^{2}

Simplify

= 3 y^{2}

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

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

\frac{d}{d x} (\frac{( 1 - sec ( x ) )}{tan ( x )})

x + \frac{1}{x ^{2}} + x^{3}

\int 5 e^{- 2 x} + 4 d x

What is (\partial)/(\partial y)(1+x^4+y^3) ?
The answer to (\partial)/(\partial y)(1+x^4+y^3) is 3y^2