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

\(f'(a) = 16 a + 7 \text{.}\)

\(f'(x) = 6 ⋅ 6 ⋅ x^{5} + 7 ⋅ 4 ⋅ x^{3} - 4 ⋅ 3 ⋅ x^{2} \text{.}\)

\(f'(x) = 36 x^{5} + 28 x^{3} - 12 x^{2} \text{.}\)

\(f'(a) = 1\frac{1}{2} ⋅ 7 ⋅ a^{6} + 7 ⋅ 3 ⋅ a^{2} + 1\frac{1}{4} \text{.}\)

\(f'(a) = 10\frac{1}{2} a^{6} + 21 a^{2} + 1\frac{1}{4} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (7 p^{5} - 3) (p - 9) = 7 p^{6} - 63 p^{5} - 3 p + 27\)

(Differentiëren)
\(f'(p) = 42 p^{5} - 315 p^{4} - 3 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (3 x^{5} + 1)^{2} = 9 x^{10} + 6 x^{5} + 1\)

(Differentiëren)
\(f'(x) = 90 x^{9} + 30 x^{4} \text{.}\)

(Productregel)
\(f'(x) = 4 (-4 x^{2} + 6 x) + (4 x + 5) (-8 x + 6) \text{.}\)

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

(Quotiëntregel)
\(f'(a) = {(5 a - 1) ⋅ -2 - (-2 a - 3) ⋅ 5 \over (5 a - 1)^{2}} \text{.}\)

\(f'(a) = {(-10 a + 2) - (-10 a - 15) \over (5 a - 1)^{2}} = {17 \over (5 a - 1)^{2}} \text{.}\)

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

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