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

\(f'(a) = 4 a + 3 \text{.}\)

\(f'(a) = 7 ⋅ 6 ⋅ a^{5} + 2 \text{.}\)

\(f'(a) = 42 a^{5} + 2 \text{.}\)

\(f'(p) = \frac{2}{5} ⋅ 9 ⋅ p^{8} + 1\frac{1}{8} ⋅ 5 ⋅ p^{4} + 1\frac{3}{4} ⋅ 3 ⋅ p^{2} + 2 \text{.}\)

\(f'(p) = 3\frac{3}{5} p^{8} + 5\frac{5}{8} p^{4} + 5\frac{1}{4} p^{2} + 2 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (6 x^{4} + 5) (x + 7) = 6 x^{5} + 42 x^{4} + 5 x + 35\)

(Differentiëren)
\(f'(x) = 30 x^{4} + 168 x^{3} + 5 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (3 x^{4} - 5)^{2} = 9 x^{8} - 30 x^{4} + 25\)

(Differentiëren)
\(f'(x) = 72 x^{7} - 120 x^{3} \text{.}\)

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

(Productregel)
\(f'(p) = (18 p + 7) (6 p^{2} + 3 p + 5) + (9 p^{2} + 7 p) (12 p + 3) \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-9 a + 8) ⋅ -1 - (-a - 8) ⋅ -9 \over (-9 a + 8)^{2}} \text{.}\)

\(f'(a) = {(9 a - 8) - (9 a + 72) \over (-9 a + 8)^{2}} = {-80 \over (-9 a + 8)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-7 a + 4) ⋅ -18 a - -9 a^{2} ⋅ -7 \over (-7 a + 4)^{2}} \text{.}\)

\(f'(a) = {(126 a^{2} - 72 a) - 63 a^{2} \over (-7 a + 4)^{2}} = {63 a^{2} - 72 a \over (-7 a + 4)^{2}} \text{.}\)