What is (\partial)/(\partial x)(4yx^3-15y^2x^4) ?

The answer to (\partial)/(\partial x)(4yx^3-15y^2x^4) is 12yx^2-60y^2x^3

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(\partial)/(\partial x)(4yx^3-15y^2x^4)

\frac{\partial}{\partial x} (4 y x^{3} - 15 y^{2} x^{4})

12 y x^{2} - 60 y^{2} x^{3}

Solution steps

\frac{\partial}{\partial x} (4 y x^{3} - 15 y^{2} x^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 y x^{3}) - \frac{\partial}{\partial x} (15 y^{2} x^{4})

\frac{\partial}{\partial x} (4 y x^{3}) = 12 y x^{2}

\frac{\partial}{\partial x} (15 y^{2} x^{4}) = 60 y^{2} x^{3}

= 12 y x^{2} - 60 y^{2} x^{3}

What is (\partial)/(\partial x)(4yx^3-15y^2x^4) ?
The answer to (\partial)/(\partial x)(4yx^3-15y^2x^4) is 12yx^2-60y^2x^3