\(f'(a) = 2 ⋅ 3 ⋅ a^{2} + 8 \text{.}\)

\(f'(a) = 6 a^{2} + 8 \text{.}\)

\(f'(a) = -8 ⋅ 8 ⋅ a^{7} + 6 ⋅ 6 ⋅ a^{5} + 4 \text{.}\)

\(f'(a) = -64 a^{7} + 36 a^{5} + 4 \text{.}\)

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

\(f'(x) = 72 x^{8} + 5\frac{1}{3} x^{7} + 5\frac{1}{3} x^{3} + 4\frac{1}{5} x^{2} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (7 p^{2} + 1) (p + 8) = 7 p^{3} + 56 p^{2} + p + 8\)

(Differentiëren)
\(f'(p) = 21 p^{2} + 112 p + 1 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{3} - 4)^{2} = 25 x^{6} - 40 x^{3} + 16\)

(Differentiëren)
\(f'(x) = 150 x^{5} - 120 x^{2} \text{.}\)

(Productregel)
\(f'(a) = -1 (8 a^{2} + 6 a) + (-a + 1) (16 a + 6) \text{.}\)

(Productregel)
\(f'(p) = (18 p - 9) (8 p^{2} - 7 p + 6) + (9 p^{2} - 9 p) (16 p - 7) \text{.}\)

(Quotiëntregel)
\(f'(a) = {(2 a - 9) ⋅ 1 - (a - 7) ⋅ 2 \over (2 a - 9)^{2}} \text{.}\)

\(f'(a) = {(2 a - 9) - (2 a - 14) \over (2 a - 9)^{2}} = {5 \over (2 a - 9)^{2}} \text{.}\)

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

\(f'(x) = {(-12 x^{2} + 8 x) - -6 x^{2} \over (6 x - 4)^{2}} = {-6 x^{2} + 8 x \over (6 x - 4)^{2}} \text{.}\)

(Herleiden)
\(f(x) = {6 \over 7 x^{4}} = \frac{6}{7} x^{-4}\)

(Differentiëren)
\(f'(x) = \frac{6}{7} ⋅ -4 ⋅ x^{-5} = -\frac{24}{7} ⋅ x^{-5}\)

(Herleiden)
\(f'(x) = -\frac{24}{7} ⋅ {1 \over x^{5}} = -{24 \over 7 x^{5}}\)

(Herleiden)
\(f(a) = -4 a ⋅ \sqrt[8]{a^{3}} = -4 ⋅ a^{1} ⋅ a^{\frac{3}{8}} = -4 ⋅ a^{1\frac{3}{8}}\)

(Differentiëren)
\(f'(a) = -4 ⋅ 1\frac{3}{8} ⋅ a^{\frac{3}{8}}\)

(Herleiden)
\(f'(a) = -5\frac{1}{2} ⋅ a^{0} ⋅ a^{\frac{3}{8}} = -5\frac{1}{2} ⋅ \sqrt[8]{a^{3}}\)

(Uitdelen)
\(f(p) = {p^{6} \over 4 p^{3}} + {2 p^{2} \over 4 p^{3}} = \frac{1}{4} p^{3} + \frac{2}{4} p^{-1}\)

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

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

(Herleiden)
\(f(x) = {3 x^{2} + 5 \over x^{\frac{1}{4}}}\)

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

(Differentiëren)
\(f'(x) = 3 ⋅ 1\frac{3}{4} ⋅ x^{\frac{3}{4}} + 5 ⋅ -\frac{1}{4} ⋅ x^{-1\frac{1}{4}}\)

(Herleiden)
\(f'(x) = 5\frac{1}{4} ⋅ \sqrt[4]{x^{3}} - {5 \over 4 x ⋅ \sqrt[4]{x}}\)

(Herleiden)
\(f(a) = {5 \over 3 \sqrt{a}} + 8 \sqrt{a} = \frac{5}{3} a^{-\frac{1}{2}} + 8 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{5}{3} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 8 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{5 \over 6 a \sqrt{a}} + {4 \over \sqrt{a}}\)

(Herleiden)
\(f(x) = {5 x + 2 \over x^{3\frac{1}{2}}}\)

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

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

(Herleiden)
\(f'(x) = -{25 \over 2 x^{3} ⋅ \sqrt{x}} - {7 \over x^{4} ⋅ \sqrt{x}}\)

(Kettingregel)
\(f'(a) = 9 ⋅ 6 ⋅ (\frac{6}{7} a + 7)^{5} ⋅ \frac{6}{7}\)

(Herleiden)
\(f'(a) = 46\frac{2}{7} (\frac{6}{7} a + 7)^{5} \text{.}\)

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

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

(Herleiden)
\(f'(p) = -40 ⋅ (4 p - 3)^{-3} = -{40 \over (4 p - 3)^{3}}\)

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

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

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

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

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

(Herleiden)
\(f'(x) = \frac{14}{3} ⋅ (4 x - 5)^{-1\frac{1}{2}} = {14 \over 3 (4 x - 5) \sqrt{4 x - 5}}\)

(Kettingregel)
\(f'(a) = 3 ⋅ 4 ⋅ (6 a^{4} + 2 a^{2} + 1)^{3} ⋅ (24 a^{3} + 4 a)\)

(Herleiden)
\(f'(a) = (288 a^{3} + 48 a) ⋅ (6 a^{4} + 2 a^{2} + 1)^{3}\)

\(f(a) = (-9 a^{2} - 4) ⋅ e^{-5 a + 2} + (-3 a^{3} - 4 a) ⋅ e^{-5 a + 2} ⋅ -5\)
\(\text{ } = (-9 a^{2} - 4) ⋅ e^{-5 a + 2} + (15 a^{3} + 20 a) ⋅ e^{-5 a + 2}\)
\(\text{ } = (15 a^{3} - 9 a^{2} + 20 a - 4) ⋅ e^{-5 a + 2}\)

\(f(p) = 5 ⋅ e^{6 p - 4} ⋅ 6 = 30 ⋅ e^{6 p - 4}\)