What is (\partial)/(\partial x)(6xcos(x)sin(y)) ?

The answer to (\partial)/(\partial x)(6xcos(x)sin(y)) is 6sin(y)(cos(x)-xsin(x))

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(\partial)/(\partial x)(6xcos(x)sin(y))

\frac{\partial}{\partial x} (6 x cos (x) sin (y))

6 sin (y) (cos (x) - x sin (x))

Solution steps

\frac{\partial}{\partial x} (6 x cos (x) sin (y))

Treat

y

as a constant

Take the constant out:

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

= 6 sin (y) \frac{\partial}{\partial x} (x cos (x))

Apply the Product Rule:

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

f = x, g = cos (x)

= 6 sin (y) (\frac{\partial}{\partial x} (x) cos (x) + \frac{\partial}{\partial x} (cos (x)) x)

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

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

= 6 sin (y) (1 \cdot cos (x) + (- sin (x)) x)

Simplify

= 6 sin (y) (cos (x) - x sin (x))

\frac{\partial}{\partial z} (4 ln (\frac{3 x y}{7 z}))

y^{^{''}} + 289 y = sec (17 x), y (0) = 3, y^{^{'}} (0) = 3

y = e^{4 x} cos (π x), (0, 1)

\frac{d}{d x} (e^{0.5 x})

\frac{d}{d x} (\frac{4 x ^{3} - 5 x ^{2}}{3 x ^{2} - 4})

What is (\partial)/(\partial x)(6xcos(x)sin(y)) ?
The answer to (\partial)/(\partial x)(6xcos(x)sin(y)) is 6sin(y)(cos(x)-xsin(x))