\(f'(a) = 3 ⋅ 2 ⋅ a^{1} \text{.}\)

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

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

\(f'(x) = -72 x^{8} + 7 x^{6} + 16 x^{3} \text{.}\)

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

\(f'(x) = 16\frac{1}{3} x^{6} + 4\frac{1}{2} x^{3} + 2\frac{1}{2} x^{2} + 2 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (9 p^{5} - 6) (p - 8) = 9 p^{6} - 72 p^{5} - 6 p + 48\)

(Differentiëren)
\(f'(p) = 54 p^{5} - 360 p^{4} - 6 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (3 a^{2} + 4)^{2} = 9 a^{4} + 24 a^{2} + 16\)

(Differentiëren)
\(f'(a) = 36 a^{3} + 48 a \text{.}\)

(Productregel)
\(f'(a) = 1 (-2 a^{2} + 3 a) + (a - 6) (-4 a + 3) \text{.}\)

(Productregel)
\(f'(p) = (-18 p + 3) (9 p^{2} - 3 p + 7) + (-9 p^{2} + 3 p) (18 p - 3) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-4 x - 5) ⋅ 3 - (3 x - 3) ⋅ -4 \over (-4 x - 5)^{2}} \text{.}\)

\(f'(x) = {(-12 x - 15) - (-12 x + 12) \over (-4 x - 5)^{2}} = {-27 \over (-4 x - 5)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(4 x + 7) ⋅ -4 x - -2 x^{2} ⋅ 4 \over (4 x + 7)^{2}} \text{.}\)

\(f'(x) = {(-16 x^{2} - 28 x) - -8 x^{2} \over (4 x + 7)^{2}} = {-8 x^{2} - 28 x \over (4 x + 7)^{2}} \text{.}\)

(Herleiden)
\(f(x) = -{5 \over 2 x^{7}} = -\frac{5}{2} x^{-7}\)

(Differentiëren)
\(f'(x) = -\frac{5}{2} ⋅ -7 ⋅ x^{-8} = \frac{35}{2} ⋅ x^{-8}\)

(Herleiden)
\(f'(x) = \frac{35}{2} ⋅ {1 \over x^{8}} = {35 \over 2 x^{8}}\)

(Herleiden)
\(f(p) = 9 p^{3} ⋅ \sqrt[4]{p^{3}} = 9 ⋅ p^{3} ⋅ p^{\frac{3}{4}} = 9 ⋅ p^{3\frac{3}{4}}\)

(Differentiëren)
\(f'(p) = 9 ⋅ 3\frac{3}{4} ⋅ p^{2\frac{3}{4}}\)

(Herleiden)
\(f'(p) = 33\frac{3}{4} ⋅ p^{2} ⋅ p^{\frac{3}{4}} = 33\frac{3}{4} p^{2} ⋅ \sqrt[4]{p^{3}}\)

(Uitdelen)
\(f(x) = {x^{7} \over 3 x^{4}} + {2 x \over 3 x^{4}} = \frac{1}{3} x^{3} + \frac{2}{3} x^{-3}\)

(Differentiëren)
\(f'(x) = \frac{1}{3} ⋅ 3 ⋅ x^{2} + \frac{2}{3} ⋅ -3 ⋅ x^{-4}\)

(Herleiden)
\(f'(x) = x^{2} - {2 \over x^{4}}\)

(Herleiden)
\(f(a) = {4 a^{3} - 1 \over a^{\frac{1}{5}}}\)

(Uitdelen)
\(f(a) = {4 a^{3} \over a^{\frac{1}{5}}} - {1 \over a^{\frac{1}{5}}} = 4 a^{2\frac{4}{5}} - a^{-\frac{1}{5}}\)

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

(Herleiden)
\(f'(a) = 11\frac{1}{5} a ⋅ \sqrt[5]{a^{4}} + {1 \over 5 a ⋅ \sqrt[5]{a}}\)

(Herleiden)
\(f(a) = {3 \over 4 \sqrt{a}} + 4 \sqrt{a} = \frac{3}{4} a^{-\frac{1}{2}} + 4 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{3}{4} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 4 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{3 \over 8 a \sqrt{a}} + {2 \over \sqrt{a}}\)

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

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

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

(Herleiden)
\(f'(p) = {15 \over 2 p^{2} ⋅ \sqrt{p}} + {5 \over 2 p^{3} ⋅ \sqrt{p}}\)

(Kettingregel)
\(f'(x) = 6 ⋅ 4 ⋅ (7 x - 2)^{3} ⋅ 7\)

(Herleiden)
\(f'(x) = 168 (7 x - 2)^{3} \text{.}\)

(Herleiden)
\(f(x) = -{2 \over (3 x - 5)^{4}} = -2 ⋅ (3 x - 5)^{-4}\)

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

(Herleiden)
\(f'(x) = 24 ⋅ (3 x - 5)^{-5} = {24 \over (3 x - 5)^{5}}\)

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

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

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

(Herleiden)
\(f(p) = {4 \over 3 \sqrt{4 p - 1}} = \frac{4}{3} ⋅ (4 p - 1)^{-\frac{1}{2}}\)

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

(Herleiden)
\(f'(p) = -\frac{8}{3} ⋅ (4 p - 1)^{-1\frac{1}{2}} = -{8 \over 3 (4 p - 1) \sqrt{4 p - 1}}\)

(Kettingregel)
\(f'(a) = 5 ⋅ 4 ⋅ (a^{4} + 3 a^{2} + 6)^{3} ⋅ (4 a^{3} + 6 a)\)

(Herleiden)
\(f'(a) = (80 a^{3} + 120 a) ⋅ (a^{4} + 3 a^{2} + 6)^{3}\)

\(f(p) = -6 p^{2} ⋅ e^{-3 p + 1} + (-2 p^{3} - 1) ⋅ e^{-3 p + 1} ⋅ -3\)
\(\text{ } = -6 p^{2} ⋅ e^{-3 p + 1} + (6 p^{3} + 3) ⋅ e^{-3 p + 1}\)
\(\text{ } = (6 p^{3} - 6 p^{2} + 3) ⋅ e^{-3 p + 1}\)

\(f(x) = 3 ⋅ e^{6 x + 2} ⋅ 6 = 18 ⋅ e^{6 x + 2}\)