\(f'(a) = 8 ⋅ 2 ⋅ a^{1} \text{.}\)

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

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

\(f'(x) = -18 x^{5} - 18 x - 7 \text{.}\)

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

\(f'(x) = 10\frac{1}{8} x^{8} + 5\frac{3}{5} x^{3} + \frac{3}{4} x^{2} \text{.}\)

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

(Differentiëren)
\(f'(p) = 16 p^{3} + 12 p^{2} - 5 \text{.}\)

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

(Differentiëren)
\(f'(a) = 64 a^{3} - 80 a \text{.}\)

(Productregel)
\(f'(x) = -5 (-6 x^{2} + 8 x) + (-5 x - 2) (-12 x + 8) \text{.}\)

(Productregel)
\(f'(x) = (-14 x + 7) (-9 x^{2} + 3 x + 6) + (-7 x^{2} + 7 x) (-18 x + 3) \text{.}\)

(Quotiëntregel)
\(f'(a) = {(a - 5) ⋅ -9 - (-9 a + 6) ⋅ 1 \over (a - 5)^{2}} \text{.}\)

\(f'(a) = {(-9 a + 45) - (-9 a + 6) \over (a - 5)^{2}} = {39 \over (a - 5)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-2 a - 7) ⋅ 12 a - 6 a^{2} ⋅ -2 \over (-2 a - 7)^{2}} \text{.}\)

\(f'(a) = {(-24 a^{2} - 84 a) - -12 a^{2} \over (-2 a - 7)^{2}} = {-12 a^{2} - 84 a \over (-2 a - 7)^{2}} \text{.}\)

(Herleiden)
\(f(a) = {9 \over 5 a^{4}} = \frac{9}{5} a^{-4}\)

(Differentiëren)
\(f'(a) = \frac{9}{5} ⋅ -4 ⋅ a^{-5} = -\frac{36}{5} ⋅ a^{-5}\)

(Herleiden)
\(f'(a) = -\frac{36}{5} ⋅ {1 \over a^{5}} = -{36 \over 5 a^{5}}\)

(Herleiden)
\(f(p) = -4 p^{3} ⋅ \sqrt[7]{p^{5}} = -4 ⋅ p^{3} ⋅ p^{\frac{5}{7}} = -4 ⋅ p^{3\frac{5}{7}}\)

(Differentiëren)
\(f'(p) = -4 ⋅ 3\frac{5}{7} ⋅ p^{2\frac{5}{7}}\)

(Herleiden)
\(f'(p) = -14\frac{6}{7} ⋅ p^{2} ⋅ p^{\frac{5}{7}} = -14\frac{6}{7} p^{2} ⋅ \sqrt[7]{p^{5}}\)

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

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

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

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

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

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

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

(Herleiden)
\(f(x) = {5 \over 8 \sqrt{x}} - 6 \sqrt{x} = \frac{5}{8} x^{-\frac{1}{2}} - 6 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{5}{8} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 6 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{5 \over 16 x \sqrt{x}} - {3 \over \sqrt{x}}\)

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

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

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

(Herleiden)
\(f'(a) = {5 \over 2 a^{3} ⋅ \sqrt{a}} + {14 \over a^{4} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(p) = 9 ⋅ 4 ⋅ (\frac{5}{9} p + 5)^{3} ⋅ \frac{5}{9}\)

(Herleiden)
\(f'(p) = 20 (\frac{5}{9} p + 5)^{3} \text{.}\)

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

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

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

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

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

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

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

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

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

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

(Herleiden)
\(f'(a) = (96 a^{3} + 120) ⋅ (a^{4} + 5 a + 3)^{5}\)

\(f(x) = 8 x ⋅ e^{-4 x + 6} + (4 x^{2} - 1) ⋅ e^{-4 x + 6} ⋅ -4\)
\(\text{ } = 8 x ⋅ e^{-4 x + 6} + (-16 x^{2} + 4) ⋅ e^{-4 x + 6}\)
\(\text{ } = (-16 x^{2} + 8 x + 4) ⋅ e^{-4 x + 6}\)

\(f(p) = 2 ⋅ e^{5 p^{3} - 6} ⋅ 15 p^{2} = 30 p^{2} ⋅ e^{5 p^{3} - 6}\)