(\partial)/(\partial y)(sqrt(x^y+ln(z)))

解

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

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

解答ステップ

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

x, z

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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