展开 ln(\sqrt[x]{x^2+y^2})

解答

展开

ln (x x^{2} + y^{2})

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

求解步骤

ln (x x^{2} + y^{2})

改写为

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

使用对数运算法则:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

假定

x \geq 0

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

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

乘以:

1 \cdot ln (x^{2} + y^{2}) = ln (x^{2} + y^{2})

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

e x p an d (2 y sin (x) + x^{2})^{5}

e x p an d - 1 + 2 (x - \frac{3 π}{4})

e x p an d (r cos (θ) - r sin (θ))^{2}

e x p an d - \frac{5 ( 5 + 41 )}{4}

s im pl i f y (4 - 14 - x) (4 + 14 - x)