What is the derivative of y=ln(5x^2+9y^2) ?

The derivative of y=ln(5x^2+9y^2) is (10x)/(5x^2+9y^2)

What is the first derivative of y=ln(5x^2+9y^2) ?

The first derivative of y=ln(5x^2+9y^2) is (10x)/(5x^2+9y^2)

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derivative of

y = ln (5 x^{2} + 9 y^{2})

\frac{10 x}{5 x ^{2} + 9 y ^{2}}

Solution steps

\frac{d}{d x} (ln (5 x^{2} + 9 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x ^{2} + 9 y ^{2}} \frac{d}{d x} (5 x^{2} + 9 y^{2})

= \frac{1}{5 x ^{2} + 9 y ^{2}} \frac{d}{d x} (5 x^{2} + 9 y^{2})

\frac{d}{d x} (5 x^{2} + 9 y^{2}) = 10 x

= \frac{1}{5 x ^{2} + 9 y ^{2}} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 9 y ^{2}} \cdot 10 x : \frac{10 x}{5 x ^{2} + 9 y ^{2}}

= \frac{10 x}{5 x ^{2} + 9 y ^{2}}

h \to 0 lim (- 2 x - h + 6)

\int 4 u d u

y = x^{3} - 4 x^{2}, y = 2 x^{2} - 8 x

f (x) = \frac{1}{35} x^{5} + \frac{1}{4} x^{4} + x + 1

\int_{1}^{2} \frac{1}{x - 2} d x

What is the derivative of y=ln(5x^2+9y^2) ?
The derivative of y=ln(5x^2+9y^2) is (10x)/(5x^2+9y^2)
What is the first derivative of y=ln(5x^2+9y^2) ?
The first derivative of y=ln(5x^2+9y^2) is (10x)/(5x^2+9y^2)