d/(d{y)}(ln(sqrt({x)^2+{y}^2+{z}^2}))

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

= \frac{1}{x ^{2} + y ^{2} + z ^{2}} \cdot \frac{y}{x ^{2} + y ^{2} + z ^{2}}

化简

\frac{1}{x ^{2} + y ^{2} + z ^{2}} \cdot \frac{y}{x ^{2} + y ^{2} + z ^{2}} : \frac{y}{x ^{2} + y ^{2} + z ^{2}}

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

f (x) = ln (2 x + 1)

t an g e n t \frac{x ^{2}}{x - 8}

\int x^{2} (x - 8)^{13} d x

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

\frac{d}{d x} (ln (8 - 3 x))