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

\(f'(a) = 18 a + 7 \text{.}\)

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

\(f'(a) = 48 a^{7} + 49 a^{6} - 30 a^{4} \text{.}\)

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

\(f'(x) = 54 x^{5} + 1\frac{3}{5} x^{3} + 1\frac{1}{2} x \text{.}\)

(Haakjes wegwerken)
\(f(p) = (8 p^{4} - 3) (p + 1) = 8 p^{5} + 8 p^{4} - 3 p - 3\)

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

(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)
\(f'(p) = -2 (5 p^{2} - 3 p) + (-2 p - 9) (10 p - 3) \text{.}\)

(Productregel)
\(f'(x) = (8 x - 2) (5 x^{2} + x - 1) + (4 x^{2} - 2 x) (10 x + 1) \text{.}\)

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

\(f'(a) = {(-81 a + 45) - (-81 a + 18) \over (9 a - 5)^{2}} = {27 \over (9 a - 5)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-5 x - 7) ⋅ -16 x - -8 x^{2} ⋅ -5 \over (-5 x - 7)^{2}} \text{.}\)

\(f'(x) = {(80 x^{2} + 112 x) - 40 x^{2} \over (-5 x - 7)^{2}} = {40 x^{2} + 112 x \over (-5 x - 7)^{2}} \text{.}\)

(Herleiden)
\(f(a) = {9 \over 8 a^{5}} = \frac{9}{8} a^{-5}\)

(Differentiëren)
\(f'(a) = \frac{9}{8} ⋅ -5 ⋅ a^{-6} = -\frac{45}{8} ⋅ a^{-6}\)

(Herleiden)
\(f'(a) = -\frac{45}{8} ⋅ {1 \over a^{6}} = -{45 \over 8 a^{6}}\)

(Herleiden)
\(f(x) = -8 x^{3} ⋅ \sqrt[7]{x^{4}} = -8 ⋅ x^{3} ⋅ x^{\frac{4}{7}} = -8 ⋅ x^{3\frac{4}{7}}\)

(Differentiëren)
\(f'(x) = -8 ⋅ 3\frac{4}{7} ⋅ x^{2\frac{4}{7}}\)

(Herleiden)
\(f'(x) = -28\frac{4}{7} ⋅ x^{2} ⋅ x^{\frac{4}{7}} = -28\frac{4}{7} x^{2} ⋅ \sqrt[7]{x^{4}}\)

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

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

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

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

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

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

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

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

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

(Herleiden)
\(f'(p) = -{2 \over 3 p \sqrt{p}} - {4 \over \sqrt{p}}\)

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

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

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

(Herleiden)
\(f'(a) = -{5 \over a^{3} ⋅ \sqrt{a}} + {35 \over 2 a^{4} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(p) = 3 ⋅ 9 ⋅ (2 p - 1)^{8} ⋅ 2\)

(Herleiden)
\(f'(p) = 54 (2 p - 1)^{8} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -24 ⋅ (3 x - 1)^{-5} = -{24 \over (3 x - 1)^{5}}\)

(Herleiden)
\(f(a) = 2 \sqrt{4 a + 5} = 2 ⋅ (4 a + 5)^{\frac{1}{2}} \text{.}\)

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

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

(Herleiden)
\(f(x) = -{5 \over 9 \sqrt{5 x - 1}} = -\frac{5}{9} ⋅ (5 x - 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = -\frac{5}{9} ⋅ -\frac{1}{2} ⋅ (5 x - 1)^{-1\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(x) = \frac{25}{18} ⋅ (5 x - 1)^{-1\frac{1}{2}} = {25 \over 18 (5 x - 1) \sqrt{5 x - 1}}\)

(Kettingregel)
\(f'(a) = 3 ⋅ 6 ⋅ (4 a^{4} + 5 a^{3} + a)^{5} ⋅ (16 a^{3} + 15 a^{2} + 1)\)

(Herleiden)
\(f'(a) = (288 a^{3} + 270 a^{2} + 18) ⋅ (4 a^{4} + 5 a^{3} + a)^{5}\)

\(f(p) = (-12 p^{2} - 2 p) ⋅ e^{6 p - 4} + (-4 p^{3} - p^{2}) ⋅ e^{6 p - 4} ⋅ 6\)
\(\text{ } = (-12 p^{2} - 2 p) ⋅ e^{6 p - 4} + (-24 p^{3} - 6 p^{2}) ⋅ e^{6 p - 4}\)
\(\text{ } = (-24 p^{3} - 18 p^{2} - 2 p) ⋅ e^{6 p - 4}\)

\(f(a) = -5 ⋅ 2^{3 a^{3} + 6 a^{2}} ⋅ \ln(2) ⋅ (9 a^{2} + 12 a) = (-45 a^{2} - 60 a) ⋅ 2^{3 a^{3} + 6 a^{2}} ⋅ \ln(2)\)