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

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

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

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

4 x^{3}

Solution steps

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

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

\frac{\partial}{\partial x} (3 y^{3}) = 0

= 4 x^{3} + 0

Simplify

= 4 x^{3}

x \to 1 lim (x^{3} - 3 x + 2)

\int \frac{1}{x + x ^{2}} d x

y^{^{''}} + \frac{1}{2} y = 0

f (x) = (5 x + 9) x^{2}

\frac{3}{x}, at x = \frac{1}{16}

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