What is the derivative of y=ln(5x^2+7y^2) ?

The derivative of y=ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)

What is the first derivative of y=ln(5x^2+7y^2) ?

The first derivative of y=ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)

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derivative of

y = ln (5 x^{2} + 7 y^{2})

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\frac{2}{t} - \frac{4}{t ^{2}}

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What is the derivative of y=ln(5x^2+7y^2) ?
The derivative of y=ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)
What is the first derivative of y=ln(5x^2+7y^2) ?
The first derivative of y=ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)