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Popular >

d/(d{y)}(ln({x}+2{y}+3{z}))

Solution

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

Solution

\frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}

Solution steps

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

Apply the chain rule:

\frac{1}{x + 2 y + 3 z} \frac{d}{d y} (x + 2 y + 3 z)

= \frac{1}{x + 2 y + 3 z} \frac{d}{d y} (x + 2 y + 3 z)

\frac{d}{d y} (x + 2 y + 3 z) = \frac{d}{d y} (x) + 2

= \frac{1}{x + 2 y + 3 z} (\frac{d}{d y} (x) + 2)

Simplify

\frac{1}{x + 2 y + 3 z} (\frac{d}{d y} (x) + 2) : \frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}

= \frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}

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Frequently Asked Questions (FAQ)

What is the d/(d{y)}(ln({x}+2{y}+3{z})) ?
The d/(d{y)}(ln({x}+2{y}+3{z})) is (d/(d{y)}({x})+2)/({x)+2{y}+3{z}}
What is the first d/(d{y)}(ln({x}+2{y}+3{z})) ?
The first d/(d{y)}(ln({x}+2{y}+3{z})) is (d/(d{y)}({x})+2)/({x)+2{y}+3{z}}