(\partial)/(\partial y)(ln(2w^3-7y+3xy^2))

解答

\frac{\partial}{\partial y} (ln (2 w^{3} - 7 y + 3 x y^{2}))

\frac{6 y x - 7}{2 w ^{3} - 7 y + 3 y ^{2} x}

求解步骤

\frac{\partial}{\partial y} (ln (2 w^{3} - 7 y + 3 x y^{2}))

将

w, x

视为常数

使用连锁律:

\frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \frac{\partial}{\partial y} (2 w^{3} - 7 y + 3 x y^{2})

= \frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \frac{\partial}{\partial y} (2 w^{3} - 7 y + 3 x y^{2})

\frac{\partial}{\partial y} (2 w^{3} - 7 y + 3 x y^{2}) = 6 x y - 7

= \frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} (6 x y - 7)

化简

\frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} (6 x y - 7) : \frac{6 y x - 7}{2 w ^{3} - 7 y + 3 y ^{2} x}

= \frac{6 y x - 7}{2 w ^{3} - 7 y + 3 y ^{2} x}

d er i v a t i v e y = \frac{6 x}{1 - tan ( x )}

\frac{\partial}{\partial x} (x^{\frac{1}{4}} \cdot y^{\frac{1}{2}})

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y \to 0 lim (\frac{sin ( y )}{y})