What is (\partial)/(\partial x)(ln(x^2+y^2+6)) ?

The answer to (\partial)/(\partial x)(ln(x^2+y^2+6)) is (2x)/(x^2+y^2+6)

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(\partial)/(\partial x)(ln(x^2+y^2+6))

\frac{\partial}{\partial x} (ln (x^{2} + y^{2} + 6))

\frac{2 x}{x ^{2} + y ^{2} + 6}

Solution steps

\frac{\partial}{\partial x} (ln (x^{2} + y^{2} + 6))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + y^{2} + 6)

= \frac{1}{x ^{2} + y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + y^{2} + 6)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 6) = 2 x

= \frac{1}{x ^{2} + y ^{2} + 6} \cdot 2 x

Simplify

\frac{1}{x ^{2} + y ^{2} + 6} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{2} + 6}

= \frac{2 x}{x ^{2} + y ^{2} + 6}

\int (5 x^{5} + 3) x^{2} d x

\frac{d y}{d x} = (5 y)

\int \frac{y ^{2} + 9}{y ^{2} + 4} d y

\frac{\partial}{\partial x} (e^{x} \cdot ln (y))

sin (x^{2})

What is (\partial)/(\partial x)(ln(x^2+y^2+6)) ?
The answer to (\partial)/(\partial x)(ln(x^2+y^2+6)) is (2x)/(x^2+y^2+6)