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Popular >

derivative of ln(x^2+y^2-1)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

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

\frac{d}{d x} (1) = 0

= \frac{2}{x} + 2 y \frac{d y}{d x} - 0

Simplify

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

Popular Examples

derivative of (((3x+1)/(x^2))^3)

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

limit as x approaches+0 of x(x-[x])

x \to + 0 lim (x (x - [x]))

(\partial)/(\partial x)(-2y^3sin(2x))

\frac{\partial}{\partial x} (- 2 y^{3} sin (2 x))

d x - x + y d y = 0

integral of e^{17x}

\int e^{17 x} d x

Frequently Asked Questions (FAQ)

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