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

The derivative of ln(2x^2+y^2) is (4x+2y\frac{dy)/(dx)}{2x^2+y^2}

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

The first derivative of ln(2x^2+y^2) is (4x+2y\frac{dy)/(dx)}{2x^2+y^2}

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

\frac{4 x + 2 y \frac{d y}{d x}}{2 x ^{2} + y ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} + y^{2}) = 4 x + 2 y \frac{d y}{d x}

= \frac{1}{2 x ^{2} + y ^{2}} (4 x + 2 y \frac{d y}{d x})

Simplify

\frac{1}{2 x ^{2} + y ^{2}} (4 x + 2 y \frac{d y}{d x}) : \frac{4 x + 2 y \frac{d y}{d x}}{2 x ^{2} + y ^{2}}

= \frac{4 x + 2 y \frac{d y}{d x}}{2 x ^{2} + y ^{2}}

25 y y^{^{'}} - 4 x = 0

\frac{d}{d x} (ln (- 1))

\int (x^{2} - 4)^{3} 2 x d x

\frac{- 12}{( 1 - x ) ^{4}}

\int sinh (8 x) d x

What is the derivative of ln(2x^2+y^2) ?
The derivative of ln(2x^2+y^2) is (4x+2y\frac{dy)/(dx)}{2x^2+y^2}
What is the first derivative of ln(2x^2+y^2) ?
The first derivative of ln(2x^2+y^2) is (4x+2y\frac{dy)/(dx)}{2x^2+y^2}