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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(x^2e^{x^2})

\frac{\partial}{\partial x} (x^{2} e^{x^{2}})

(\partial)/(\partial x)(e^xsin(xy))

\frac{\partial}{\partial x} (e^{x} sin (x y))

(\partial)/(\partial x)(x+y+z)

\frac{\partial}{\partial x} (x + y + z)

(\partial)/(\partial x)((4x-y^2)^{3/2})

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

sum from n=1 to infinity of 6/(2^n)

n = 1 \sum \infty \frac{6}{2 ^{n}}

Frequently Asked Questions (FAQ)

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