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

The answer to (\partial)/(\partial z)(sqrt(x^y+ln(z))) is 1/(2zsqrt(x^y+ln(z)))

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

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

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

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is (\partial)/(\partial z)(sqrt(x^y+ln(z))) ?
The answer to (\partial)/(\partial z)(sqrt(x^y+ln(z))) is 1/(2zsqrt(x^y+ln(z)))