What is the first (x-sin(x))^' ?

The first (x-sin(x))^' is 1-cos(x)

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(x-sin(x))^'

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

1 - cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

x^{'} = 1

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

= 1 - cos (x)

\frac{1}{s ^{2} + 25}

f (x) = x^{3} - 5 x^{2}

\frac{\partial}{\partial x} (e^{y} + 4 x^{3} y)

\frac{- 1}{s}

\int - cos (3 x) d x