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Popular >

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

Solution

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

Solution

\frac{2 x}{x ^{2} + y ^{2} + z ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{2} + y ^{2} + z ^{2}} \cdot 2 x

Simplify

\frac{1}{x ^{2} + y ^{2} + z ^{2}} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{2} + z ^{2}}

= \frac{2 x}{x ^{2} + y ^{2} + z ^{2}}

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Frequently Asked Questions (FAQ)

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