What is (\partial)/(\partial x)(3xcos(xy)) ?

The answer to (\partial)/(\partial x)(3xcos(xy)) is 3(cos(xy)-xysin(xy))

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(\partial)/(\partial x)(3xcos(xy))

\frac{\partial}{\partial x} (3 x cos (x y))

3 (cos (x y) - x y sin (x y))

Solution steps

\frac{\partial}{\partial x} (3 x cos (x y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{\partial}{\partial x} (x cos (x y))

Apply the Product Rule:

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

f = x, g = cos (x y)

= 3 (\frac{\partial}{\partial x} (x) cos (x y) + \frac{\partial}{\partial x} (cos (x y)) x)

\frac{\partial}{\partial x} (x) = 1

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

= 3 (1 \cdot cos (x y) + (- sin (x y) y) x)

Simplify

= 3 (cos (x y) - x y sin (x y))

g (x) = x (x^{3} - x)

\int (\frac{d y}{1}) d x

\int \frac{2 x ^{2} + 3 x + 3}{( x + 1 ) ^{3}} d x

\int_{0}^{\frac{π}{2}} cos^{6} (x) d x

\frac{d}{d x} (- sin (5 x) \cdot 5)

What is (\partial)/(\partial x)(3xcos(xy)) ?
The answer to (\partial)/(\partial x)(3xcos(xy)) is 3(cos(xy)-xysin(xy))