What is (\partial)/(\partial x)(ln(8x^2+7y^2+9)) ?

The answer to (\partial)/(\partial x)(ln(8x^2+7y^2+9)) is (16x)/(8x^2+7y^2+9)

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(\partial)/(\partial x)(ln(8x^2+7y^2+9))

\frac{\partial}{\partial x} (ln (8 x^{2} + 7 y^{2} + 9))

\frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}

Solution steps

\frac{\partial}{\partial x} (ln (8 x^{2} + 7 y^{2} + 9))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{8 x ^{2} + 7 y ^{2} + 9} \frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9)

= \frac{1}{8 x ^{2} + 7 y ^{2} + 9} \frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9)

\frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9) = 16 x

= \frac{1}{8 x ^{2} + 7 y ^{2} + 9} \cdot 16 x

Simplify

\frac{1}{8 x ^{2} + 7 y ^{2} + 9} \cdot 16 x : \frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}

= \frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}

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What is (\partial)/(\partial x)(ln(8x^2+7y^2+9)) ?
The answer to (\partial)/(\partial x)(ln(8x^2+7y^2+9)) is (16x)/(8x^2+7y^2+9)