What is the (f(t)+g(t))' ?

The (f(t)+g(t))' is f'(t)+g'(t)

What is the first (f(t)+g(t))' ?

The first (f(t)+g(t))' is f'(t)+g'(t)

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(f (t) + g (t))^{'}

f' (t) + g' (t)

Solution steps

(f (t) + g (t))^{'}

Apply the Sum/Difference Rule:

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

= f^{^{'}} (t) + g^{^{'}} (t)

= f^{^{'}} (t) + g^{^{'}} (t)

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

\int \frac{( 2 + e ^{x} ) ^{2}}{e ^{x}} d x