\(f'(a) = 3 ⋅ 2 ⋅ a^{1} + 9 \text{.}\)

\(f'(a) = 6 a + 9 \text{.}\)

\(f'(a) = 5 ⋅ a^{4} + 9 ⋅ 4 ⋅ a^{3} - 2 \text{.}\)

\(f'(a) = 5 a^{4} + 36 a^{3} - 2 \text{.}\)

\(f'(x) = 7 ⋅ 3 ⋅ x^{2} + \frac{8}{9} \text{.}\)

\(f'(x) = 21 x^{2} + \frac{8}{9} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (8 x^{4} + 7) (x + 1) = 8 x^{5} + 8 x^{4} + 7 x + 7\)

(Differentiëren)
\(f'(x) = 40 x^{4} + 32 x^{3} + 7 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (3 p^{2} - 1)^{2} = 9 p^{4} - 6 p^{2} + 1\)

(Differentiëren)
\(f'(p) = 36 p^{3} - 12 p \text{.}\)

(Productregel)
\(f'(a) = -4 (-6 a^{2} + a) + (-4 a - 2) (-12 a + 1) \text{.}\)

(Productregel)
\(f'(x) = (14 x - 9) (-8 x^{2} + 6 x - 4) + (7 x^{2} - 9 x) (-16 x + 6) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-9 x - 6) ⋅ 4 - (4 x + 9) ⋅ -9 \over (-9 x - 6)^{2}} \text{.}\)

\(f'(x) = {(-36 x - 24) - (-36 x - 81) \over (-9 x - 6)^{2}} = {57 \over (-9 x - 6)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(5 a + 4) ⋅ -8 a - -4 a^{2} ⋅ 5 \over (5 a + 4)^{2}} \text{.}\)

\(f'(a) = {(-40 a^{2} - 32 a) - -20 a^{2} \over (5 a + 4)^{2}} = {-20 a^{2} - 32 a \over (5 a + 4)^{2}} \text{.}\)