\(f'(a) = 6 ⋅ 2 ⋅ a^{1} \text{.}\)

\(f'(a) = 12 a \text{.}\)

\(f'(x) = 7 ⋅ 3 ⋅ x^{2} + 4 ⋅ 2 ⋅ x^{1} - 3 \text{.}\)

\(f'(x) = 21 x^{2} + 8 x - 3 \text{.}\)

\(f'(a) = 1\frac{3}{5} ⋅ 6 ⋅ a^{5} + 1\frac{1}{3} ⋅ 5 ⋅ a^{4} + 3\frac{1}{2} ⋅ 4 ⋅ a^{3} \text{.}\)

\(f'(a) = 9\frac{3}{5} a^{5} + 6\frac{2}{3} a^{4} + 14 a^{3} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{2} + 8) (x - 3) = 5 x^{3} - 15 x^{2} + 8 x - 24\)

(Differentiëren)
\(f'(x) = 15 x^{2} - 30 x + 8 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (3 p^{5} + 4)^{2} = 9 p^{10} + 24 p^{5} + 16\)

(Differentiëren)
\(f'(p) = 90 p^{9} + 120 p^{4} \text{.}\)

(Productregel)
\(f'(a) = 1 (-7 a^{2} + 9 a) + (a - 6) (-14 a + 9) \text{.}\)

(Productregel)
\(f'(p) = (-2 p - 6) (7 p^{2} - 4 p - 8) + (-p^{2} - 6 p) (14 p - 4) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(9 x - 7) ⋅ 5 - (5 x + 3) ⋅ 9 \over (9 x - 7)^{2}} \text{.}\)

\(f'(x) = {(45 x - 35) - (45 x + 27) \over (9 x - 7)^{2}} = {-62 \over (9 x - 7)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(7 x - 6) ⋅ 18 x - 9 x^{2} ⋅ 7 \over (7 x - 6)^{2}} \text{.}\)

\(f'(x) = {(126 x^{2} - 108 x) - 63 x^{2} \over (7 x - 6)^{2}} = {63 x^{2} - 108 x \over (7 x - 6)^{2}} \text{.}\)