What is the derivative of (x/(x+1))cos(x) ?

The derivative of (x/(x+1))cos(x) is (cos(x))/((x+1)^2)-(xsin(x))/(x+1)

What is the first derivative of (x/(x+1))cos(x) ?

The first derivative of (x/(x+1))cos(x) is (cos(x))/((x+1)^2)-(xsin(x))/(x+1)

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derivative of

(\frac{x}{x + 1}) cos (x)

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

Solution steps

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

Apply the Product Rule:

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

f = \frac{x}{x + 1}, g = cos (x)

= \frac{d}{d x} (\frac{x}{x + 1}) cos (x) + \frac{d}{d x} (cos (x)) \frac{x}{x + 1}

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

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

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

Simplify

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

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

4 - 3 u^{2}

60 t^{2} - 60 t

13 e^{- x}

x^{x} - 100

\frac{( x + 6 )}{x}

What is the derivative of (x/(x+1))cos(x) ?
The derivative of (x/(x+1))cos(x) is (cos(x))/((x+1)^2)-(xsin(x))/(x+1)
What is the first derivative of (x/(x+1))cos(x) ?
The first derivative of (x/(x+1))cos(x) is (cos(x))/((x+1)^2)-(xsin(x))/(x+1)