What is (\partial)/(\partial x)(ln(x^2+9y^2+6)) ?

The answer to (\partial)/(\partial x)(ln(x^2+9y^2+6)) is (2x)/(x^2+9y^2+6)

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(\partial)/(\partial x)(ln(x^2+9y^2+6))

\frac{\partial}{\partial x} (ln (x^{2} + 9 y^{2} + 6))

\frac{2 x}{x ^{2} + 9 y ^{2} + 6}

Solution steps

\frac{\partial}{\partial x} (ln (x^{2} + 9 y^{2} + 6))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + 9 y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + 9 y^{2} + 6)

= \frac{1}{x ^{2} + 9 y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + 9 y^{2} + 6)

\frac{\partial}{\partial x} (x^{2} + 9 y^{2} + 6) = 2 x

= \frac{1}{x ^{2} + 9 y ^{2} + 6} \cdot 2 x

Simplify

\frac{1}{x ^{2} + 9 y ^{2} + 6} \cdot 2 x : \frac{2 x}{x ^{2} + 9 y ^{2} + 6}

= \frac{2 x}{x ^{2} + 9 y ^{2} + 6}

\int_{0}^{1} 24 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

x \to 0 lim (e^{\frac{- 1}{x}})

\int \frac{x ^{2}}{( 3 - x ^{3} ) ^{2}} d x

\frac{d}{d x} (5 (- csc^{2} (x) + sec^{2} (x)))

\int x csc (2 x) cot (2 x) d x

What is (\partial)/(\partial x)(ln(x^2+9y^2+6)) ?
The answer to (\partial)/(\partial x)(ln(x^2+9y^2+6)) is (2x)/(x^2+9y^2+6)