What is (\partial)/(\partial x)(7xcos(x)cos(y)) ?

The answer to (\partial)/(\partial x)(7xcos(x)cos(y)) is 7cos(y)(cos(x)-xsin(x))

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(\partial)/(\partial x)(7xcos(x)cos(y))

\frac{\partial}{\partial x} (7 x cos (x) cos (y))

7 cos (y) (cos (x) - x sin (x))

Solution steps

\frac{\partial}{\partial x} (7 x cos (x) cos (y))

Treat

y

as a constant

Take the constant out:

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

= 7 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)

= 7 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)

= 7 cos (y) (1 \cdot cos (x) + (- sin (x)) x)

Simplify

= 7 cos (y) (cos (x) - x sin (x))

\frac{d y}{d t} = 8 - \frac{y}{200 + 3 t}

7 e^{x} cos (x)

f (x) = - 2 x e^{x^{2}}, at x = 2

n = 4 \sum \infty \frac{x ^{n}}{n ^{5}}

x - 1 (x^{2} + 1)

What is (\partial)/(\partial x)(7xcos(x)cos(y)) ?
The answer to (\partial)/(\partial x)(7xcos(x)cos(y)) is 7cos(y)(cos(x)-xsin(x))