What is the derivative of ln(x^2+y^3) ?

The derivative of ln(x^2+y^3) is (2x+3y^2\frac{dy)/(dx)}{x^2+y^3}

What is the first derivative of ln(x^2+y^3) ?

The first derivative of ln(x^2+y^3) is (2x+3y^2\frac{dy)/(dx)}{x^2+y^3}

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\frac{d}{d x} (ln (x^{2} + y^{3}))

\frac{2 x + 3 y ^{2} \frac{d y}{d x}}{x ^{2} + y ^{3}}

Solution steps

\frac{d}{d x} (ln (x^{2} + y^{3}))

Apply the chain rule:

\frac{1}{x ^{2} + y ^{3}} \frac{d}{d x} (x^{2} + y^{3})

= \frac{1}{x ^{2} + y ^{3}} \frac{d}{d x} (x^{2} + y^{3})

\frac{d}{d x} (x^{2} + y^{3}) = 2 x + 3 y^{2} \frac{d y}{d x}

= \frac{1}{x ^{2} + y ^{3}} (2 x + 3 y^{2} \frac{d y}{d x})

Simplify

\frac{1}{x ^{2} + y ^{3}} (2 x + 3 y^{2} \frac{d y}{d x}) : \frac{2 x + 3 y ^{2} \frac{d y}{d x}}{x ^{2} + y ^{3}}

= \frac{2 x + 3 y ^{2} \frac{d y}{d x}}{x ^{2} + y ^{3}}

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

\int \frac{5 x ^{3} - 3 x ^{2} + 2}{2 x ^{2}} d x

\int_{0}^{3} 1 + x^{2} d x

x \to 6 + lim (6 x - 6)

y = \frac{x}{4} - \frac{4}{x}

What is the derivative of ln(x^2+y^3) ?
The derivative of ln(x^2+y^3) is (2x+3y^2\frac{dy)/(dx)}{x^2+y^3}
What is the first derivative of ln(x^2+y^3) ?
The first derivative of ln(x^2+y^3) is (2x+3y^2\frac{dy)/(dx)}{x^2+y^3}