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

The answer to (\partial)/(\partial z)(x^{y^z}) is y^zx^{y^z}ln(x)ln(y)

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

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

y^{z} x^{y^{z}} ln (x) ln (y)

Solution steps

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

Treat

x, y

as constants

Apply exponent rule:

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

x^{y^{z}} = e^{y^{z} l n (x)}

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

Apply the chain rule:

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

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

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

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

e^{y^{z} l n (x)} = x^{y^{z}}

= y^{z} x^{y^{z}} ln (x) ln (y)

y^{^{'}} = (- 4 y + 44)^{\frac{1}{2}}

y^{^{'}} - 5 y = (cos (x)) \cdot e^{5 x}

\frac{1}{2} y^{^{'}} + y = 0

\frac{d}{d x} (sin (x - 1))

\int cos (t) d t

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