\(f'(a) = 9 ⋅ 3 ⋅ a^{2} \text{.}\)

\(f'(a) = 27 a^{2} \text{.}\)

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

\(f'(p) = 32 p^{7} + 6 p \text{.}\)

\(f'(x) = \frac{2}{5} ⋅ 8 ⋅ x^{7} + 1\frac{1}{7} ⋅ 6 ⋅ x^{5} + \frac{3}{4} ⋅ 2 ⋅ x^{1} + 9 \text{.}\)

\(f'(x) = 3\frac{1}{5} x^{7} + 6\frac{6}{7} x^{5} + 1\frac{1}{2} x + 9 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (6 a^{3} + 9) (a - 2) = 6 a^{4} - 12 a^{3} + 9 a - 18\)

(Differentiëren)
\(f'(a) = 24 a^{3} - 36 a^{2} + 9 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{3} - 1)^{2} = 16 x^{6} - 8 x^{3} + 1\)

(Differentiëren)
\(f'(x) = 96 x^{5} - 24 x^{2} \text{.}\)

(Herleiden)
\(f(p) = -{3 \over 7 p^{3}} = -\frac{3}{7} p^{-3}\)

(Differentiëren)
\(f'(p) = -\frac{3}{7} ⋅ -3 ⋅ p^{-4} = \frac{9}{7} ⋅ p^{-4}\)

(Herleiden)
\(f'(p) = \frac{9}{7} ⋅ {1 \over p^{4}} = {9 \over 7 p^{4}}\)

(Herleiden)
\(f(x) = -7 x^{3} ⋅ \sqrt[9]{x^{8}} = -7 ⋅ x^{3} ⋅ x^{\frac{8}{9}} = -7 ⋅ x^{3\frac{8}{9}}\)

(Differentiëren)
\(f'(x) = -7 ⋅ 3\frac{8}{9} ⋅ x^{2\frac{8}{9}}\)

(Herleiden)
\(f'(x) = -27\frac{2}{9} ⋅ x^{2} ⋅ x^{\frac{8}{9}} = -27\frac{2}{9} x^{2} ⋅ \sqrt[9]{x^{8}}\)

(Uitdelen)
\(f(a) = {a^{6} \over 3 a^{3}} + {5 a \over 3 a^{3}} = \frac{1}{3} a^{3} + \frac{5}{3} a^{-2}\)

(Differentiëren)
\(f'(a) = \frac{1}{3} ⋅ 3 ⋅ a^{2} + \frac{5}{3} ⋅ -2 ⋅ a^{-3}\)

(Herleiden)
\(f'(a) = a^{2} - {10 \over 3 a^{3}}\)

(Herleiden)
\(f(x) = {x^{2} + 4 \over x^{\frac{1}{5}}}\)

(Uitdelen)
\(f(x) = {x^{2} \over x^{\frac{1}{5}}} + {4 \over x^{\frac{1}{5}}} = x^{1\frac{4}{5}} + 4 x^{-\frac{1}{5}}\)

(Differentiëren)
\(f'(x) = 1\frac{4}{5} ⋅ x^{\frac{4}{5}} + 4 ⋅ -\frac{1}{5} ⋅ x^{-1\frac{1}{5}}\)

(Herleiden)
\(f'(x) = 1\frac{4}{5} ⋅ \sqrt[5]{x^{4}} - {4 \over 5 x ⋅ \sqrt[5]{x}}\)

(Herleiden)
\(f(a) = {2 \over 5 \sqrt{a}} - 7 \sqrt{a} = \frac{2}{5} a^{-\frac{1}{2}} - 7 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{2}{5} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} - 7 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{1 \over 5 a \sqrt{a}} - {7 \over 2 \sqrt{a}}\)

(Herleiden)
\(f(p) = {-5 p - 4 \over p^{1\frac{1}{2}}}\)

(Uitdelen)
\(f(p) = {-5 p \over p^{1\frac{1}{2}}} - {4 \over p^{1\frac{1}{2}}} = -5 p^{-\frac{1}{2}} - 4 p^{-1\frac{1}{2}}\)

(Differentiëren)
\(f'(p) = -5 ⋅ -\frac{1}{2} ⋅ p^{-1\frac{1}{2}} - 4 ⋅ -1\frac{1}{2} ⋅ p^{-2\frac{1}{2}}\)

(Herleiden)
\(f'(p) = {5 \over 2 p ⋅ \sqrt{p}} + {6 \over p^{2} ⋅ \sqrt{p}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 4 ⋅ (6 a - 9)^{3} ⋅ 6\)

(Herleiden)
\(f'(a) = 48 (6 a - 9)^{3} \text{.}\)

(Herleiden)
\(f(a) = {5 \over (2 a - 1)^{3}} = 5 ⋅ (2 a - 1)^{-3}\)

(Kettingregel)
\(f'(a) = 5 ⋅ -3 ⋅ (2 a - 1)^{-4} ⋅ 2\)

(Herleiden)
\(f'(a) = -30 ⋅ (2 a - 1)^{-4} = -{30 \over (2 a - 1)^{4}}\)

(Herleiden)
\(f(x) = -\frac{4}{7} \sqrt{3 x - 5} = -\frac{4}{7} ⋅ (3 x - 5)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(x) = -\frac{4}{7} ⋅ \frac{1}{2} ⋅ (3 x - 5)^{-\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(x) = -\frac{6}{7} ⋅ (3 x - 5)^{-\frac{1}{2}} = -{6 \over 7 \sqrt{3 x - 5}}\)

(Herleiden)
\(f(p) = {4 \over 5 \sqrt{4 p - 1}} = \frac{4}{5} ⋅ (4 p - 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(p) = \frac{4}{5} ⋅ -\frac{1}{2} ⋅ (4 p - 1)^{-1\frac{1}{2}} ⋅ 4\)

(Herleiden)
\(f'(p) = -\frac{8}{5} ⋅ (4 p - 1)^{-1\frac{1}{2}} = -{8 \over 5 (4 p - 1) \sqrt{4 p - 1}}\)