What is (\partial)/(\partial x)(log_{e}(x^2+y^4)) ?

The answer to (\partial)/(\partial x)(log_{e}(x^2+y^4)) is (2x)/(x^2+y^4)

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(\partial)/(\partial x)(log_{e}(x^2+y^4))

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{4}))

\frac{2 x}{x ^{2} + y ^{4}}

Solution steps

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{4}))

Simplify

lo g_{e} (x^{2} + y^{4}) : ln (x^{2} + y^{4})

= \frac{\partial}{\partial x} (ln (x^{2} + y^{4}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + y ^{4}} \frac{\partial}{\partial x} (x^{2} + y^{4})

= \frac{1}{x ^{2} + y ^{4}} \frac{\partial}{\partial x} (x^{2} + y^{4})

\frac{\partial}{\partial x} (x^{2} + y^{4}) = 2 x

= \frac{1}{x ^{2} + y ^{4}} \cdot 2 x

Simplify

\frac{1}{x ^{2} + y ^{4}} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{4}}

= \frac{2 x}{x ^{2} + y ^{4}}

What is (\partial)/(\partial x)(log_{e}(x^2+y^4)) ?
The answer to (\partial)/(\partial x)(log_{e}(x^2+y^4)) is (2x)/(x^2+y^4)