What is (\partial)/(\partial x)(sqrt(xy)+b^{xy}) ?

The answer to (\partial)/(\partial x)(sqrt(xy)+b^{xy}) is (sqrt(y))/(2sqrt(x))+yb^{yx}ln(b)

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(\partial)/(\partial x)(sqrt(xy)+b^{xy})

\frac{\partial}{\partial x} (x y + b^{x y})

\frac{y}{2 x} + y b^{y x} ln (b)

Solution steps

\frac{\partial}{\partial x} (x y + b^{x y})

Treat

y, b

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (b^{x y})

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

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

= \frac{y}{2 x} + y b^{y x} ln (b)

\frac{d y}{d x} = \frac{x - 1}{y ^{3}}

x \to + 2 lim (\frac{( 1 )}{( x + 2 )})

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

\frac{d}{d x} (\frac{4 - x}{5 x})

\int \frac{( ln ( x ) ) ^{32}}{x} d x

What is (\partial)/(\partial x)(sqrt(xy)+b^{xy}) ?
The answer to (\partial)/(\partial x)(sqrt(xy)+b^{xy}) is (sqrt(y))/(2sqrt(x))+yb^{yx}ln(b)