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

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

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

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

4 x^{3} - 2 y^{3} x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 4 x^{3} - 2 y^{3} x

6 - 5 x^{3}

6 x^{2} y^{2} d x + 4 x^{3} y d y = 0

y = 5 x, x = 5, y = \frac{5}{x}, x = 0

\int tan^{2} (5 x) d x

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

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