What is (\partial)/(\partial x)(2^{xy}) ?

The answer to (\partial)/(\partial x)(2^{xy}) is ln(2)*2^{xy}y

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(\partial)/(\partial x)(2^{xy})

\frac{\partial}{\partial x} (2^{x y})

ln (2) \cdot 2^{x y} y

Solution steps

\frac{\partial}{\partial x} (2^{x y})

Treat

y

as a constant

Apply exponent rule:

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

2^{x y} = e^{x y l n (2)}

= \frac{\partial}{\partial x} (e^{x y l n (2)})

Apply the chain rule:

e^{x y l n (2)} \frac{\partial}{\partial x} (x y ln (2))

= e^{x y l n (2)} \frac{\partial}{\partial x} (x y ln (2))

\frac{\partial}{\partial x} (x y ln (2)) = ln (2) y

= e^{x y l n (2)} ln (2) y

e^{x y l n (2)} = 2^{x y}

= ln (2) \cdot 2^{x y} y

f (x) = \frac{2}{( 1 - x ) ^{3}}

\frac{\partial}{\partial x} (e^{\frac{x ^{2}}{2}})

f (x) = \frac{- 8 x}{x ^{2} + 1}, (1, - 4)

y^{^{''}} + 3.26 y^{^{'}} + 2.66 y = 0

\frac{\partial}{\partial x} (e^{x} (x + 2 y))

What is (\partial)/(\partial x)(2^{xy}) ?
The answer to (\partial)/(\partial x)(2^{xy}) is ln(2)*2^{xy}y