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

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

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

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

3 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 x^{2} - 0

Simplify

= 3 x^{2}

f (x) = x^{3} - 6 x^{2} - 34 x + 40, at x = 4

\frac{\partial}{\partial x} (9 x sin (6 x^{2} y))

y = \frac{5 x}{1 + x ^{2}}, (5, \frac{25}{26})

f (x) = (\frac{x + 5}{x ^{2} + 2})^{2}

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