What is the derivative of ln(7x^2+9y^2) ?

The derivative of ln(7x^2+9y^2) is (14x+18y\frac{dy)/(dx)}{7x^2+9y^2}

What is the first derivative of ln(7x^2+9y^2) ?

The first derivative of ln(7x^2+9y^2) is (14x+18y\frac{dy)/(dx)}{7x^2+9y^2}

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\frac{d}{d x} (ln (7 x^{2} + 9 y^{2}))

\frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}

Solution steps

\frac{d}{d x} (ln (7 x^{2} + 9 y^{2}))

Apply the chain rule:

\frac{1}{7 x ^{2} + 9 y ^{2}} \frac{d}{d x} (7 x^{2} + 9 y^{2})

= \frac{1}{7 x ^{2} + 9 y ^{2}} \frac{d}{d x} (7 x^{2} + 9 y^{2})

\frac{d}{d x} (7 x^{2} + 9 y^{2}) = 14 x + 18 y \frac{d y}{d x}

= \frac{1}{7 x ^{2} + 9 y ^{2}} (14 x + 18 y \frac{d y}{d x})

Simplify

\frac{1}{7 x ^{2} + 9 y ^{2}} (14 x + 18 y \frac{d y}{d x}) : \frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}

= \frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}

x \to 1 lim (\frac{1}{x + 3})

\int \frac{2 v}{1 - v ^{2}} d v

\int_{0}^{100} e^{- 0.01 x} d x

\frac{x y ^{^{'}}}{e ^{x} + 1} = 2

f (x) = 3 x^{2} - 24 x + 45

What is the derivative of ln(7x^2+9y^2) ?
The derivative of ln(7x^2+9y^2) is (14x+18y\frac{dy)/(dx)}{7x^2+9y^2}
What is the first derivative of ln(7x^2+9y^2) ?
The first derivative of ln(7x^2+9y^2) is (14x+18y\frac{dy)/(dx)}{7x^2+9y^2}