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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{- 1}^{2} (3 x^{2} - 2 x + 3) d x

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

(e^{x + 2})^{^{'}}

\frac{d}{d z} (x^{y^{z}})

n = 0 \sum \infty 1 - (0.2)^{n}

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