What is (\partial)/(\partial x)(x^3(1+y)+z^2) ?

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

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(\partial)/(\partial x)(x^3(1+y)+z^2)

\frac{\partial}{\partial x} (x^{3} (1 + y) + z^{2})

3 x^{2} (y + 1)

Solution steps

\frac{\partial}{\partial x} (x^{3} (1 + y) + z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} (1 + y)) + \frac{\partial}{\partial x} (z^{2})

\frac{\partial}{\partial x} (x^{3} (1 + y)) = 3 x^{2} (1 + y)

\frac{\partial}{\partial x} (z^{2}) = 0

= 3 x^{2} (1 + y) + 0

Simplify

= 3 x^{2} (y + 1)

\frac{d}{d x} (\frac{x ^{2}}{( 5 + x )})

arctan (x) - \frac{π}{4}

\frac{\partial}{\partial x} (\frac{x ^{2}}{1 + y ^{2}})

x \to 35 lim (\frac{x ^{2}}{5} - \frac{7}{x})

\frac{d}{d x} (- x^{2} - 4 x - 2)

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