\(f'(p) = 3 ⋅ 3 ⋅ p^{2} + 4 \text{.}\)

\(f'(p) = 9 p^{2} + 4 \text{.}\)

\(f'(a) = -8 ⋅ 7 ⋅ a^{6} - 6 ⋅ 3 ⋅ a^{2} - 3 ⋅ 2 ⋅ a^{1} \text{.}\)

\(f'(a) = -56 a^{6} - 18 a^{2} - 6 a \text{.}\)

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

\(f'(x) = 12 x^{7} + 3\frac{3}{4} x^{2} + 1\frac{1}{2} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (7 a^{4} + 8) (a - 3) = 7 a^{5} - 21 a^{4} + 8 a - 24\)

(Differentiëren)
\(f'(a) = 35 a^{4} - 84 a^{3} + 8 \text{.}\)

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

(Differentiëren)
\(f'(x) = 100 x^{3} - 60 x \text{.}\)

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

(Productregel)
\(f'(p) = (14 p + 5) (8 p^{2} - p - 2) + (7 p^{2} + 5 p) (16 p - 1) \text{.}\)

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

\(f'(x) = {(27 x + 18) - (27 x + 21) \over (3 x + 2)^{2}} = {-3 \over (3 x + 2)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-6 a + 5) ⋅ -10 a - -5 a^{2} ⋅ -6 \over (-6 a + 5)^{2}} \text{.}\)

\(f'(a) = {(60 a^{2} - 50 a) - 30 a^{2} \over (-6 a + 5)^{2}} = {30 a^{2} - 50 a \over (-6 a + 5)^{2}} \text{.}\)