What is (\partial)/(\partial x)(xln(y)-y^22^{xy}) ?

The answer to (\partial)/(\partial x)(xln(y)-y^22^{xy}) is ln(y)-y^2e^{xyln(2)}ln(2)y

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(\partial)/(\partial x)(xln(y)-y^22^{xy})

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

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

Solution steps

\frac{\partial}{\partial x} (x ln (y) - y^{2} \cdot 2^{x y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

y^{^{''}} + 9 y = - sin (3 x)

\int_{0}^{1} \frac{1}{x ^{2} - 2 x + 2} d x

\frac{\partial}{\partial φ} (ρ sin (φ) sin (θ))

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{2 x}}{x ^{2}}

x \to a lim (sin (x))

What is (\partial)/(\partial x)(xln(y)-y^22^{xy}) ?
The answer to (\partial)/(\partial x)(xln(y)-y^22^{xy}) is ln(y)-y^2e^{xyln(2)}ln(2)y