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

The derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}

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

The first derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of ln(x+y^2) ?
The derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}
What is the first derivative of ln(x+y^2) ?
The first derivative of ln(x+y^2) is (1+2y\frac{dy)/(dx)}{x+y^2}