What is (\partial)/(\partial x)(3xcos(x)cos(y)) ?

The answer to (\partial)/(\partial x)(3xcos(x)cos(y)) is 3cos(y)(cos(x)-xsin(x))

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(\partial)/(\partial x)(3xcos(x)cos(y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 3 cos (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)

= 3 cos (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)

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

Simplify

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

x - 6

\int \frac{x ^{4}}{5 - x ^{5}} d x

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

\int (x^{2} \cdot ln (x)) d x

\frac{1}{t ^{4}}

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