What is the first (1+cos(x))^' ?

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

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(1+cos(x))^'

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

- sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

= 1^{^{'}} + (cos (x))^{^{'}}

1^{'} = 0

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

= 0 - sin (x)

Simplify

= - sin (x)

\int_{0}^{3} ∣ x - 1 ∣ d x

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

\int_{0}^{5} π (2 x)^{2} d x

\int \frac{( sec ^{2} ( x ) )}{tan ^{2} ( x )} d x

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