What is the first (t-sin(t))^' ?

The first (t-sin(t))^' is 1-cos(t)

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(t-sin(t))^'

(t - sin (t))^{^{'}}

1 - cos (t)

Solution steps

(t - sin (t))^{'}

Apply the Sum/Difference Rule:

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

= t^{^{'}} - (sin (t))^{^{'}}

t^{'} = 1

(sin (t))^{'} = cos (t)

= 1 - cos (t)

\frac{d}{d x} (lo g_{2} (x^{2}))

x^{2}, 2, 5

n = 1 \sum \infty \frac{4}{n ln ( 8 n )}

ln (x^{4})

f (x) = \frac{sec ( x )}{1 + tan ( x )}