What is the first d/(dy)(x-5ln|x|+yx) ?

The first d/(dy)(x-5ln|x|+yx) is x

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d/(dy)(x-5ln|x|+yx)

\frac{d}{d y} (x - 5 ln ∣ x ∣ + y x)

x

Solution steps

\frac{d}{d y} (x - 5 ln ∣ x ∣ + y x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d x}{d y} - \frac{d}{d y} (5 ln ∣ x ∣) + \frac{d}{d y} (y x)

\frac{d x}{d y} = 0

\frac{d}{d y} (5 ln ∣ x ∣) = 0

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

= 0 - 0 + x

Simplify

= x

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