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

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

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

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

z x^{yz} ln (x)

Solution steps

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

Treat

x, z

as constants

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= z x^{yz} ln (x)

\frac{\partial}{\partial x} (ln (9 x^{2} + 4 y^{2} + 5))

\frac{\partial}{\partial y} (x^{3} - 2 x y + 15)

\int x arcsec (2 x) d x

\int \frac{1}{e ^{- v} + 1} d v

\int x^{3} \cdot sin (2 x) d x

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