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

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

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(\partial)/(\partial x)(x^2*cos(xy))

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

2 x cos (x y) - x^{2} y sin (x y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = cos (x y)

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

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

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

= 2 x cos (x y) + (- sin (x y) y) x^{2}

Simplify

= 2 x cos (x y) - x^{2} y sin (x y)

y = 10 x^{2}, y^{2} = \frac{1}{10} x

x \to 3 - lim (\frac{1}{( x - 3 ) ^{2}})

\int \frac{1}{2 x 16 x ^{2} - 8} d x

\int 4^{3 x} d x

6 t^{2} + 8

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