What is the derivative of ln(3x^2+5y^2) ?

The derivative of ln(3x^2+5y^2) is (6x+10y\frac{dy)/(dx)}{3x^2+5y^2}

What is the first derivative of ln(3x^2+5y^2) ?

The first derivative of ln(3x^2+5y^2) is (6x+10y\frac{dy)/(dx)}{3x^2+5y^2}

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\frac{d}{d x} (ln (3 x^{2} + 5 y^{2}))

\frac{6 x + 10 y \frac{d y}{d x}}{3 x ^{2} + 5 y ^{2}}

Solution steps

\frac{d}{d x} (ln (3 x^{2} + 5 y^{2}))

Apply the chain rule:

\frac{1}{3 x ^{2} + 5 y ^{2}} \frac{d}{d x} (3 x^{2} + 5 y^{2})

= \frac{1}{3 x ^{2} + 5 y ^{2}} \frac{d}{d x} (3 x^{2} + 5 y^{2})

\frac{d}{d x} (3 x^{2} + 5 y^{2}) = 6 x + 10 y \frac{d y}{d x}

= \frac{1}{3 x ^{2} + 5 y ^{2}} (6 x + 10 y \frac{d y}{d x})

Simplify

\frac{1}{3 x ^{2} + 5 y ^{2}} (6 x + 10 y \frac{d y}{d x}) : \frac{6 x + 10 y \frac{d y}{d x}}{3 x ^{2} + 5 y ^{2}}

= \frac{6 x + 10 y \frac{d y}{d x}}{3 x ^{2} + 5 y ^{2}}

\frac{d}{d x} (\frac{x + 5}{x + 2})

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

\frac{\partial}{\partial x} (x \cdot arcsin (\frac{y}{x}))

\frac{10}{( s + 4 ) ( s + 2 ) ^{3}}

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

What is the derivative of ln(3x^2+5y^2) ?
The derivative of ln(3x^2+5y^2) is (6x+10y\frac{dy)/(dx)}{3x^2+5y^2}
What is the first derivative of ln(3x^2+5y^2) ?
The first derivative of ln(3x^2+5y^2) is (6x+10y\frac{dy)/(dx)}{3x^2+5y^2}