\(f'(a) = 9 ⋅ 3 ⋅ a^{2} + 8 \text{.}\)

\(f'(a) = 27 a^{2} + 8 \text{.}\)

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

\(f'(x) = 45 x^{8} - 16 x^{7} - 30 x^{4} + 28 x^{3} \text{.}\)

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

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

(Haakjes wegwerken)
\(f(x) = (9 x^{4} - 8) (x + 1) = 9 x^{5} + 9 x^{4} - 8 x - 8\)

(Differentiëren)
\(f'(x) = 45 x^{4} + 36 x^{3} - 8 \text{.}\)

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

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

(Productregel)
\(f'(a) = 7 (-2 a^{2} + 2 a) + (7 a - 9) (-4 a + 2) \text{.}\)

(Productregel)
\(f'(x) = (-8 x - 8) (7 x^{2} - 5 x + 8) + (-4 x^{2} - 8 x) (14 x - 5) \text{.}\)

(Quotiëntregel)
\(f'(p) = {(-6 p + 3) ⋅ -2 - (-2 p + 1) ⋅ -6 \over (-6 p + 3)^{2}} \text{.}\)

\(f'(p) = {(12 p - 6) - (12 p - 6) \over (-6 p + 3)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-8 x + 6) ⋅ 6 x - 3 x^{2} ⋅ -8 \over (-8 x + 6)^{2}} \text{.}\)

\(f'(x) = {(-48 x^{2} + 36 x) - -24 x^{2} \over (-8 x + 6)^{2}} = {-24 x^{2} + 36 x \over (-8 x + 6)^{2}} \text{.}\)

(Herleiden)
\(f(a) = {8 \over 7 a^{8}} = \frac{8}{7} a^{-8}\)

(Differentiëren)
\(f'(a) = \frac{8}{7} ⋅ -8 ⋅ a^{-9} = -\frac{64}{7} ⋅ a^{-9}\)

(Herleiden)
\(f'(a) = -\frac{64}{7} ⋅ {1 \over a^{9}} = -{64 \over 7 a^{9}}\)

(Herleiden)
\(f(p) = 9 p ⋅ \sqrt[9]{p^{5}} = 9 ⋅ p^{1} ⋅ p^{\frac{5}{9}} = 9 ⋅ p^{1\frac{5}{9}}\)

(Differentiëren)
\(f'(p) = 9 ⋅ 1\frac{5}{9} ⋅ p^{\frac{5}{9}}\)

(Herleiden)
\(f'(p) = 14 ⋅ p^{0} ⋅ p^{\frac{5}{9}} = 14 ⋅ \sqrt[9]{p^{5}}\)

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

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

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

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

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

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

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

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

(Differentiëren)
\(f'(a) = \frac{9}{5} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 5 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{9 \over 10 a \sqrt{a}} + {5 \over 2 \sqrt{a}}\)

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

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

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

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

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

(Herleiden)
\(f'(x) = 168 (6 x - 3)^{6} \text{.}\)

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

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

(Herleiden)
\(f'(x) = 30 ⋅ (5 x + 4)^{-3} = {30 \over (5 x + 4)^{3}}\)

(Herleiden)
\(f(a) = -\frac{3}{8} \sqrt{2 a - 5} = -\frac{3}{8} ⋅ (2 a - 5)^{\frac{1}{2}} \text{.}\)

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

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

(Herleiden)
\(f(p) = -{9 \over 4 \sqrt{3 p + 5}} = -\frac{9}{4} ⋅ (3 p + 5)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(p) = -\frac{9}{4} ⋅ -\frac{1}{2} ⋅ (3 p + 5)^{-1\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(p) = \frac{27}{8} ⋅ (3 p + 5)^{-1\frac{1}{2}} = {27 \over 8 (3 p + 5) \sqrt{3 p + 5}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 5 ⋅ (4 a^{3} + 6 a^{2} + 3 a)^{4} ⋅ (12 a^{2} + 12 a + 3)\)

(Herleiden)
\(f'(a) = (120 a^{2} + 120 a + 30) ⋅ (4 a^{3} + 6 a^{2} + 3 a)^{4}\)

\(f(a) = 2 ⋅ 5^{-6 a^{3} + 3 a} ⋅ \ln(5) ⋅ (-18 a^{2} + 3) = (-36 a^{2} + 6) ⋅ 5^{-6 a^{3} + 3 a} ⋅ \ln(5)\)

\(f(a) = (9 a^{2} - 1) ⋅ e^{a - 5} + (3 a^{3} - a) ⋅ e^{a - 5} ⋅ 1\)
\(\text{ } = (9 a^{2} - 1) ⋅ e^{a - 5} + (3 a^{3} - a) ⋅ e^{a - 5}\)
\(\text{ } = (3 a^{3} + 9 a^{2} - a - 1) ⋅ e^{a - 5}\)