What is (\partial)/(\partial x)((z)(x^2ln(y)-z)) ?

The answer to (\partial)/(\partial x)((z)(x^2ln(y)-z)) is 2zxln(y)

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(\partial)/(\partial x)((z)(x^2ln(y)-z))

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

2 z x ln (y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 x ln (y) - 0)

Simplify

= 2 z x ln (y)

(a - 1, b) (a + 1, b + 1)

\frac{2 - 14 x ^{\frac{12}{7}}}{7 x ^{\frac{5}{7}}}

(s + 0.8 + 0.43 i) (s + 0.8) (s - 0.43 i) (s + 0.6)

2 e^{- x} x - e^{- x} (x^{2} - 17)

(t - 2) cos (2 π t)

What is (\partial)/(\partial x)((z)(x^2ln(y)-z)) ?
The answer to (\partial)/(\partial x)((z)(x^2ln(y)-z)) is 2zxln(y)