What is the derivative of x*cos(((x)/((x-2)))) ?

The derivative of x*cos(((x)/((x-2)))) is cos(x/(x-2))+(2xsin(x/(x-2)))/((x-2)^2)

What is the first derivative of x*cos(((x)/((x-2)))) ?

The first derivative of x*cos(((x)/((x-2)))) is cos(x/(x-2))+(2xsin(x/(x-2)))/((x-2)^2)

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\frac{d}{d x} (x \cdot cos (\frac{( x )}{( x - 2 )}))

cos (\frac{x}{x - 2}) + \frac{2 x sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (x cos (\frac{( x )}{( x - 2 )}))

Apply the Product Rule:

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

f = x, g = cos (\frac{x}{x - 2})

= \frac{d x}{d x} cos (\frac{x}{x - 2}) + \frac{d}{d x} (cos (\frac{x}{x - 2})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (\frac{x}{x - 2})) = \frac{2 sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}}

= 1 \cdot cos (\frac{x}{x - 2}) + \frac{2 sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}} x

Simplify

1 \cdot cos (\frac{x}{x - 2}) + \frac{2 sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}} x : cos (\frac{x}{x - 2}) + \frac{2 x sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}}

= cos (\frac{x}{x - 2}) + \frac{2 x sin ( \frac{x}{x - 2} )}{( x - 2 ) ^{2}}

x \to 0 lim (- e^{x})

x^{2} y^{^{'}} = (x + 1) y

\int_{- 1}^{0} \frac{1}{1 + x ^{2}} d x

\int_{0}^{1} - 1 (x^{2} + 1) e^{- x} d x

\frac{\partial}{\partial x} (7 - 3 x^{2} - 3 y^{2})

What is the derivative of x*cos(((x)/((x-2)))) ?
The derivative of x*cos(((x)/((x-2)))) is cos(x/(x-2))+(2xsin(x/(x-2)))/((x-2)^2)
What is the first derivative of x*cos(((x)/((x-2)))) ?
The first derivative of x*cos(((x)/((x-2)))) is cos(x/(x-2))+(2xsin(x/(x-2)))/((x-2)^2)