What is the (xcos(x))^' ?

The (xcos(x))^' is cos(x)-xsin(x)

What is the first (xcos(x))^' ?

The first (xcos(x))^' is cos(x)-xsin(x)

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(x cos (x))^{^{'}}

cos (x) - x sin (x)

Solution steps

(x cos (x))^{'}

Apply the Product Rule:

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

f = x, g = cos (x)

= x^{^{'}} cos (x) + (cos (x))^{^{'}} x

x^{'} = 1

(cos (x))^{'} = - sin (x)

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

Simplify

= cos (x) - x sin (x)

f (x) = x^{3} (3 - x^{2})

f (x) = \frac{x}{x ^{2} - 7}

\int \frac{2 x}{( x - 3 ) ^{2}} d x

n \to 2 lim (\frac{1}{n ^{2}})

x \to 2 + lim (x^{2} - 4)