What is (\partial)/(\partial x)(3xln(y)+yln(z)-2x) ?

The answer to (\partial)/(\partial x)(3xln(y)+yln(z)-2x) is 3ln(y)-2

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(\partial)/(\partial x)(3xln(y)+yln(z)-2x)

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

3 ln (y) - 2

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x ln (y)) = 3 ln (y)

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

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

= 3 ln (y) + 0 - 2

Simplify

= 3 ln (y) - 2

\int x (x + \frac{1}{x}) d x

\int x^{2} d x

x \to 0 + lim (\frac{2 x}{∣ x ∣})

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

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

What is (\partial)/(\partial x)(3xln(y)+yln(z)-2x) ?
The answer to (\partial)/(\partial x)(3xln(y)+yln(z)-2x) is 3ln(y)-2