What is (\partial)/(\partial x)(3xln(y)+yln(z)-4x) ?

The answer to (\partial)/(\partial x)(3xln(y)+yln(z)-4x) is 3ln(y)-4

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(\partial)/(\partial x)(3xln(y)+yln(z)-4x)

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

3 ln (y) - 4

Solution steps

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 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} (4 x)

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

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

\frac{\partial}{\partial x} (4 x) = 4

= 3 ln (y) + 0 - 4

Simplify

= 3 ln (y) - 4

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

\int 2 x (x^{2} + 1)^{- 4} d x

\frac{7}{s ^{3} + 2 s ^{2} + 9 s + 18}

\int \frac{e ^{x}}{e ^{- 6 x}} d x

\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

What is (\partial)/(\partial x)(3xln(y)+yln(z)-4x) ?
The answer to (\partial)/(\partial x)(3xln(y)+yln(z)-4x) is 3ln(y)-4