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

解答

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

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

求解步骤

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

使用连锁律:

\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})

化简

\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}}

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

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

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

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

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