What is (\partial)/(\partial x)(1+x^4+y^3) ?

The answer to (\partial)/(\partial x)(1+x^4+y^3) is 4x^3

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(\partial)/(\partial x)(1+x^4+y^3)

\frac{\partial}{\partial x} (1 + x^{4} + y^{3})

4 x^{3}

Solution steps

\frac{\partial}{\partial x} (1 + x^{4} + y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (y^{3})

\frac{\partial}{\partial x} (1) = 0

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

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

= 0 + 4 x^{3} + 0

Simplify

= 4 x^{3}

\int \frac{1}{x ^{4} + 16} d x

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\int_{0}^{5} 6 x - x^{2} d x

What is (\partial)/(\partial x)(1+x^4+y^3) ?
The answer to (\partial)/(\partial x)(1+x^4+y^3) is 4x^3