What is (\partial)/(\partial x)(xy-z^2+17x^2z) ?

The answer to (\partial)/(\partial x)(xy-z^2+17x^2z) is 34xz+y

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(\partial)/(\partial x)(xy-z^2+17x^2z)

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

34 x z + y

Solution steps

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

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} (z^{2}) + \frac{\partial}{\partial x} (17 x^{2} z)

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

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

\frac{\partial}{\partial x} (17 x^{2} z) = 34 z x

= y - 0 + 34 z x

Simplify

= 34 x z + y

y = - x^{2} + 4 x + 2, (3, 5)

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

\frac{\partial}{\partial x} (4 x sin (6 x^{2} y))

\frac{d y}{d x} = x y - x

y^{^{''}} + 2 y^{^{'}} - 3 y = 0

What is (\partial)/(\partial x)(xy-z^2+17x^2z) ?
The answer to (\partial)/(\partial x)(xy-z^2+17x^2z) is 34xz+y