\(f'(a) = 6 ⋅ 2 ⋅ a^{1} \text{.}\)

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

\(f'(a) = 6 ⋅ 3 ⋅ a^{2} - 2 ⋅ 2 ⋅ a^{1} - 8 \text{.}\)

\(f'(a) = 18 a^{2} - 4 a - 8 \text{.}\)

\(f'(p) = \frac{1}{5} ⋅ 9 ⋅ p^{8} + \frac{2}{3} ⋅ 5 ⋅ p^{4} + 1\frac{1}{7} \text{.}\)

\(f'(p) = 1\frac{4}{5} p^{8} + 3\frac{1}{3} p^{4} + 1\frac{1}{7} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (9 x^{3} - 7) (x - 2) = 9 x^{4} - 18 x^{3} - 7 x + 14\)

(Differentiëren)
\(f'(x) = 36 x^{3} - 54 x^{2} - 7 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (3 x^{5} + 2)^{2} = 9 x^{10} + 12 x^{5} + 4\)

(Differentiëren)
\(f'(x) = 90 x^{9} + 60 x^{4} \text{.}\)

(Productregel)
\(f'(x) = -5 (-9 x^{2} + 9 x) + (-5 x + 4) (-18 x + 9) \text{.}\)

(Productregel)
\(f'(a) = (-12 a - 3) (9 a^{2} + a - 8) + (-6 a^{2} - 3 a) (18 a + 1) \text{.}\)

(Quotiëntregel)
\(f'(a) = {(2 a - 9) ⋅ -2 - (-2 a - 3) ⋅ 2 \over (2 a - 9)^{2}} \text{.}\)

\(f'(a) = {(-4 a + 18) - (-4 a - 6) \over (2 a - 9)^{2}} = {24 \over (2 a - 9)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(p) = {(-2 p - 7) ⋅ -16 p - -8 p^{2} ⋅ -2 \over (-2 p - 7)^{2}} \text{.}\)

\(f'(p) = {(32 p^{2} + 112 p) - 16 p^{2} \over (-2 p - 7)^{2}} = {16 p^{2} + 112 p \over (-2 p - 7)^{2}} \text{.}\)