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

The answer to (\partial)/(\partial x)(4xln(y)+yln(z)-x) is 4ln(y)-1

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

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

4 ln (y) - 1

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (x) = 1

= 4 ln (y) + 0 - 1

Simplify

= 4 ln (y) - 1

x \to 0 lim ((1 - ln (x))^{x})

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

\int \frac{1}{3} e^{x + 3} d x

5 x + 1, at x = 3

\frac{d}{d x} - \frac{3 x ^{2} sin ( \frac{x ^{3}}{4} )}{4}

What is (\partial)/(\partial x)(4xln(y)+yln(z)-x) ?
The answer to (\partial)/(\partial x)(4xln(y)+yln(z)-x) is 4ln(y)-1