What is (\partial)/(\partial x)(xy+yz^2+xz^3) ?

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

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(\partial)/(\partial x)(xy+yz^2+xz^3)

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

y + z^{3}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x y) = y

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

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

= y + 0 + z^{3}

Simplify

= y + z^{3}

\frac{\partial}{\partial x} ((x + z) e^{x - y})

\int \frac{1}{( 6 x - 1 ) ^{2}} d x

\frac{d}{d x} (- 16 x^{2})

\frac{\partial}{\partial z} (9 z e^{x yz})

\frac{d}{d x} ((1 + cos (x)) sin (x))

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