What is (\partial)/(\partial x)(x*cos(x)) ?

The answer to (\partial)/(\partial x)(x*cos(x)) is cos(x)-xsin(x)

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(\partial)/(\partial x)(x*cos(x))

\frac{\partial}{\partial x} (x \cdot cos (x))

cos (x) - x sin (x)

Solution steps

\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)

= \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)

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

Simplify

= cos (x) - x sin (x)

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

y = 6 4 + x

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

o 2 x 2 - 3 x + 2

What is (\partial)/(\partial x)(x*cos(x)) ?
The answer to (\partial)/(\partial x)(x*cos(x)) is cos(x)-xsin(x)