What is (\partial)/(\partial x)(4x^6+xy^3+2y^4) ?

The answer to (\partial)/(\partial x)(4x^6+xy^3+2y^4) is 24x^5+y^3

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(\partial)/(\partial x)(4x^6+xy^3+2y^4)

\frac{\partial}{\partial x} (4 x^{6} + x y^{3} + 2 y^{4})

24 x^{5} + y^{3}

Solution steps

\frac{\partial}{\partial x} (4 x^{6} + x y^{3} + 2 y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{6}) + \frac{\partial}{\partial x} (x y^{3}) + \frac{\partial}{\partial x} (2 y^{4})

\frac{\partial}{\partial x} (4 x^{6}) = 24 x^{5}

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

\frac{\partial}{\partial x} (2 y^{4}) = 0

= 24 x^{5} + y^{3} + 0

Simplify

= 24 x^{5} + y^{3}

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What is (\partial)/(\partial x)(4x^6+xy^3+2y^4) ?
The answer to (\partial)/(\partial x)(4x^6+xy^3+2y^4) is 24x^5+y^3