What is (\partial)/(\partial x)(y^2-cos(xy)) ?

The answer to (\partial)/(\partial x)(y^2-cos(xy)) is ysin(yx)

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(\partial)/(\partial x)(y^2-cos(xy))

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

y sin (y x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (cos (x y)) = - sin (x y) y

= 0 - (- sin (x y) y)

Simplify

= y sin (y x)

\frac{d y}{d x} y = (3 x - 2 x^{2})^{3}

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

e^{\frac{1}{6} x^{6}}, 0

x \to - 6 - lim (- \frac{1}{x + 6})

\int_{1}^{3} (3 - x)^{2} d x

What is (\partial)/(\partial x)(y^2-cos(xy)) ?
The answer to (\partial)/(\partial x)(y^2-cos(xy)) is ysin(yx)