What is (\partial)/(\partial x)(ln(5x^2+4y^2+7)) ?

The answer to (\partial)/(\partial x)(ln(5x^2+4y^2+7)) is (10x)/(5x^2+4y^2+7)

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(\partial)/(\partial x)(ln(5x^2+4y^2+7))

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

\frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

Solution steps

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7) = 10 x

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x : \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

= \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

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

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z

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(3 + 3 x^{2}) \frac{d y}{d x} + 2 x y = 2 x y^{4}

What is (\partial)/(\partial x)(ln(5x^2+4y^2+7)) ?
The answer to (\partial)/(\partial x)(ln(5x^2+4y^2+7)) is (10x)/(5x^2+4y^2+7)