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

\(f'(x) = 15 x^{2} + 9 \text{.}\)

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

\(f'(p) = -45 p^{8} - 56 p^{6} + 30 p^{4} + 9 \text{.}\)

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

\(f'(a) = \frac{1}{2} a + 4 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (2 x^{4} + 6) (x + 9) = 2 x^{5} + 18 x^{4} + 6 x + 54\)

(Differentiëren)
\(f'(x) = 10 x^{4} + 72 x^{3} + 6 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (2 a^{3} - 1)^{2} = 4 a^{6} - 4 a^{3} + 1\)

(Differentiëren)
\(f'(a) = 24 a^{5} - 12 a^{2} \text{.}\)

(Productregel)
\(f'(a) = 7 (9 a^{2} + 2 a) + (7 a + 8) (18 a + 2) \text{.}\)

(Productregel)
\(f'(p) = (-10 p - 3) (-7 p^{2} + 8 p + 5) + (-5 p^{2} - 3 p) (-14 p + 8) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(3 x - 1) ⋅ 8 - (8 x - 5) ⋅ 3 \over (3 x - 1)^{2}} \text{.}\)

\(f'(x) = {(24 x - 8) - (24 x - 15) \over (3 x - 1)^{2}} = {7 \over (3 x - 1)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(7 a - 2) ⋅ 8 a - 4 a^{2} ⋅ 7 \over (7 a - 2)^{2}} \text{.}\)

\(f'(a) = {(56 a^{2} - 16 a) - 28 a^{2} \over (7 a - 2)^{2}} = {28 a^{2} - 16 a \over (7 a - 2)^{2}} \text{.}\)

(Herleiden)
\(f(a) = -{7 \over 3 a^{6}} = -\frac{7}{3} a^{-6}\)

(Differentiëren)
\(f'(a) = -\frac{7}{3} ⋅ -6 ⋅ a^{-7} = 14 ⋅ a^{-7}\)

(Herleiden)
\(f'(a) = 14 ⋅ {1 \over a^{7}} = {14 \over a^{7}}\)

(Herleiden)
\(f(p) = -4 p^{3} ⋅ \sqrt[9]{p^{4}} = -4 ⋅ p^{3} ⋅ p^{\frac{4}{9}} = -4 ⋅ p^{3\frac{4}{9}}\)

(Differentiëren)
\(f'(p) = -4 ⋅ 3\frac{4}{9} ⋅ p^{2\frac{4}{9}}\)

(Herleiden)
\(f'(p) = -13\frac{7}{9} ⋅ p^{2} ⋅ p^{\frac{4}{9}} = -13\frac{7}{9} p^{2} ⋅ \sqrt[9]{p^{4}}\)

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

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

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

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

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

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

(Herleiden)
\(f'(x) = 9\frac{1}{2} x^{3} ⋅ \sqrt[4]{x^{3}} + {3 \over 4 x ⋅ \sqrt[4]{x}}\)

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

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

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

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

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

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

(Herleiden)
\(f'(a) = {6 \over a^{2} ⋅ \sqrt{a}} - {5 \over 2 a^{3} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(p) = 7 ⋅ 8 ⋅ (\frac{3}{7} p + 1)^{7} ⋅ \frac{3}{7}\)

(Herleiden)
\(f'(p) = 24 (\frac{3}{7} p + 1)^{7} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -60 ⋅ (4 x + 2)^{-4} = -{60 \over (4 x + 2)^{4}}\)

(Herleiden)
\(f(a) = \frac{6}{7} \sqrt{5 a - 4} = \frac{6}{7} ⋅ (5 a - 4)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(a) = \frac{6}{7} ⋅ \frac{1}{2} ⋅ (5 a - 4)^{-\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(a) = \frac{15}{7} ⋅ (5 a - 4)^{-\frac{1}{2}} = {15 \over 7 \sqrt{5 a - 4}}\)

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

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

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

(Kettingregel)
\(f'(x) = 2 ⋅ 4 ⋅ (3 x^{4} + 5 x^{3} + x)^{3} ⋅ (12 x^{3} + 15 x^{2} + 1)\)

(Herleiden)
\(f'(x) = (96 x^{3} + 120 x^{2} + 8) ⋅ (3 x^{4} + 5 x^{3} + x)^{3}\)

\(f(p) = -10 p ⋅ e^{-6 p - 2} + (-5 p^{2} + 3) ⋅ e^{-6 p - 2} ⋅ -6\)
\(\text{ } = -10 p ⋅ e^{-6 p - 2} + (30 p^{2} - 18) ⋅ e^{-6 p - 2}\)
\(\text{ } = (30 p^{2} - 10 p - 18) ⋅ e^{-6 p - 2}\)

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