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Popular >

d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y})))

Solution

\frac{d}{d x} ((z (x)) (x y + y ln (x y)))

Solution

z (x) (y + \frac{y}{x})

Solution steps

\frac{d}{d x} ((z (x)) (x y + y ln (x y)))

Take the constant out:

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

= z (x) \frac{d}{d x} (x y + y ln (x y))

Apply the Sum/Difference Rule:

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

= z (x) (\frac{d}{d x} (x y) + \frac{d}{d x} (y ln (x y)))

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

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

= z (x) (y + \frac{y}{x})

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Frequently Asked Questions (FAQ)

What is the d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y}))) ?
The d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y}))) is {z}(x)({y}+({y})/({x)})
What is the first d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y}))) ?
The first d/(d{x)}(({z}(x))({x}{y}+{y}ln({x}{y}))) is {z}(x)({y}+({y})/({x)})