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

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

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

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

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derivative of

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}}

\frac{\partial}{\partial x} (sin (π))

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{2}} d x

\int e^{2 x} - x^{2} - 1 d x

\frac{d}{d x} (cos (2 x))

y^{^{'}} = y (x y^{2} + 1)

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