What is (\partial)/(\partial x)(5^{xy}) ?

The answer to (\partial)/(\partial x)(5^{xy}) is ln(5)*5^{xy}y

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(\partial)/(\partial x)(5^{xy})

\frac{\partial}{\partial x} (5^{x y})

ln (5) \cdot 5^{x y} y

Solution steps

\frac{\partial}{\partial x} (5^{x y})

Treat

y

as a constant

Apply exponent rule:

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

5^{x y} = e^{x y l n (5)}

= \frac{\partial}{\partial x} (e^{x y l n (5)})

Apply the chain rule:

e^{x y l n (5)} \frac{\partial}{\partial x} (x y ln (5))

= e^{x y l n (5)} \frac{\partial}{\partial x} (x y ln (5))

\frac{\partial}{\partial x} (x y ln (5)) = ln (5) y

= e^{x y l n (5)} ln (5) y

e^{x y l n (5)} = 5^{x y}

= ln (5) \cdot 5^{x y} y

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What is (\partial)/(\partial x)(5^{xy}) ?
The answer to (\partial)/(\partial x)(5^{xy}) is ln(5)*5^{xy}y