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

The answer to (\partial)/(\partial x)(1+x^3+y^4) is 3x^2

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

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

3 x^{2}

Solution steps

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

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

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

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

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

= 0 + 3 x^{2} + 0

Simplify

= 3 x^{2}

\int \frac{3 x + 4}{x + 3} d x

\int_{0}^{1} - 10 (x^{2} + 1) e^{- x} d x

\frac{d y}{d x} = \frac{( x ^{2} - y )}{x}

\int x + 2 x d x d x

x \to 0 + lim (x^{2} - x - ln (x))

What is (\partial)/(\partial x)(1+x^3+y^4) ?
The answer to (\partial)/(\partial x)(1+x^3+y^4) is 3x^2