\(f'(x) = 2 ⋅ 2 ⋅ x^{1} + 4 \text{.}\)

\(f'(x) = 4 x + 4 \text{.}\)

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

\(f'(x) = 9 x^{8} + 64 x^{7} - 35 x^{6} - 24 x^{5} \text{.}\)

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

\(f'(p) = 21 p^{6} + 6\frac{1}{4} p^{4} + \frac{6}{7} p^{2} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (7 a^{2} - 5) (a + 3) = 7 a^{3} + 21 a^{2} - 5 a - 15\)

(Differentiëren)
\(f'(a) = 21 a^{2} + 42 a - 5 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (3 a^{2} + 5)^{2} = 9 a^{4} + 30 a^{2} + 25\)

(Differentiëren)
\(f'(a) = 36 a^{3} + 60 a \text{.}\)

(Productregel)
\(f'(p) = -3 (7 p^{2} + 5 p) + (-3 p + 1) (14 p + 5) \text{.}\)

(Productregel)
\(f'(x) = (16 x + 4) (-6 x^{2} - 3 x + 2) + (8 x^{2} + 4 x) (-12 x - 3) \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-4 a - 1) ⋅ -3 - (-3 a - 7) ⋅ -4 \over (-4 a - 1)^{2}} \text{.}\)

\(f'(a) = {(12 a + 3) - (12 a + 28) \over (-4 a - 1)^{2}} = {-25 \over (-4 a - 1)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-6 a - 8) ⋅ 8 a - 4 a^{2} ⋅ -6 \over (-6 a - 8)^{2}} \text{.}\)

\(f'(a) = {(-48 a^{2} - 64 a) - -24 a^{2} \over (-6 a - 8)^{2}} = {-24 a^{2} - 64 a \over (-6 a - 8)^{2}} \text{.}\)

(Herleiden)
\(f(p) = {3 \over 7 p^{9}} = \frac{3}{7} p^{-9}\)

(Differentiëren)
\(f'(p) = \frac{3}{7} ⋅ -9 ⋅ p^{-10} = -\frac{27}{7} ⋅ p^{-10}\)

(Herleiden)
\(f'(p) = -\frac{27}{7} ⋅ {1 \over p^{10}} = -{27 \over 7 p^{10}}\)

(Herleiden)
\(f(x) = -3 x ⋅ \sqrt[8]{x^{5}} = -3 ⋅ x^{1} ⋅ x^{\frac{5}{8}} = -3 ⋅ x^{1\frac{5}{8}}\)

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

(Herleiden)
\(f'(x) = -4\frac{7}{8} ⋅ x^{0} ⋅ x^{\frac{5}{8}} = -4\frac{7}{8} ⋅ \sqrt[8]{x^{5}}\)

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

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

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

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

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

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

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

(Herleiden)
\(f(x) = {8 \over 9 \sqrt{x}} + 8 \sqrt{x} = \frac{8}{9} x^{-\frac{1}{2}} + 8 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{8}{9} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} + 8 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{4 \over 9 x \sqrt{x}} + {4 \over \sqrt{x}}\)

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

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

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

(Herleiden)
\(f'(a) = -{1 \over a ⋅ \sqrt{a}} - {15 \over 2 a^{2} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(x) = 5 ⋅ 6 ⋅ (7 x + 4)^{5} ⋅ 7\)

(Herleiden)
\(f'(x) = 210 (7 x + 4)^{5} \text{.}\)

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

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

(Herleiden)
\(f'(a) = 6 ⋅ (3 a - 5)^{-3} = {6 \over (3 a - 5)^{3}}\)

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

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

(Herleiden)
\(f'(a) = -6 ⋅ (4 a + 1)^{-\frac{1}{2}} = -{6 \over \sqrt{4 a + 1}}\)

(Herleiden)
\(f(p) = -{5 \over 6 \sqrt{5 p + 3}} = -\frac{5}{6} ⋅ (5 p + 3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(p) = -\frac{5}{6} ⋅ -\frac{1}{2} ⋅ (5 p + 3)^{-1\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(p) = \frac{25}{12} ⋅ (5 p + 3)^{-1\frac{1}{2}} = {25 \over 12 (5 p + 3) \sqrt{5 p + 3}}\)

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

(Herleiden)
\(f'(x) = (360 x^{2} + 48) ⋅ (5 x^{3} + 2 x + 1)^{3}\)

\(f(x) = -6 ⋅ 2^{5 x^{3} + x} ⋅ \ln(2) ⋅ (15 x^{2} + 1) = (-90 x^{2} - 6) ⋅ 2^{5 x^{3} + x} ⋅ \ln(2)\)

\(f(x) = 5 ⋅ e^{2 x - 6} + (5 x + 2) ⋅ e^{2 x - 6} ⋅ 2\)
\(\text{ } = 5 ⋅ e^{2 x - 6} + (10 x + 4) ⋅ e^{2 x - 6}\)
\(\text{ } = (10 x + 9) ⋅ e^{2 x - 6}\)