What is (\partial)/(\partial z)(x^{yz}) ?

The answer to (\partial)/(\partial z)(x^{yz}) is yx^{yz}ln(x)

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(\partial)/(\partial z)(x^{yz})

\frac{\partial}{\partial z} (x^{yz})

y x^{yz} ln (x)

Solution steps

\frac{\partial}{\partial z} (x^{yz})

Treat

x, y

as constants

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{yz} = e^{yz l n (x)}

= \frac{\partial}{\partial z} (e^{yz l n (x)})

Apply the chain rule:

e^{yz l n (x)} \frac{\partial}{\partial z} (yz ln (x))

= e^{yz l n (x)} \frac{\partial}{\partial z} (yz ln (x))

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

= e^{yz l n (x)} y ln (x)

e^{yz l n (x)} = x^{yz}

= y x^{yz} ln (x)

\frac{d}{d x} (11 arccot (x) + 11 arccot (\frac{1}{x}))

\frac{- 5}{( 2 x ^{3} + 7 ) ^{2}}

(2, 7), (- 5, 2)

y^{^{''}} - 9 y^{^{'}} = 0

\int sin (2 x) 1 + cos^{2} (x) d x

What is (\partial)/(\partial z)(x^{yz}) ?
The answer to (\partial)/(\partial z)(x^{yz}) is yx^{yz}ln(x)