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

\(f'(a) = 12 a + 9 \text{.}\)

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

\(f'(x) = 81 x^{8} - 15 x^{4} - 6 \text{.}\)

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

\(f'(x) = 16 x^{7} + 12 x^{5} + 2\frac{2}{9} x^{4} + 3\frac{3}{7} x^{2} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (3 p^{2} - 7) (p + 9) = 3 p^{3} + 27 p^{2} - 7 p - 63\)

(Differentiëren)
\(f'(p) = 9 p^{2} + 54 p - 7 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (5 a^{3} - 2)^{2} = 25 a^{6} - 20 a^{3} + 4\)

(Differentiëren)
\(f'(a) = 150 a^{5} - 60 a^{2} \text{.}\)

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

(Differentiëren)
\(f'(a) = \frac{9}{5} ⋅ -9 ⋅ a^{-10} = -\frac{81}{5} ⋅ a^{-10}\)

(Herleiden)
\(f'(a) = -\frac{81}{5} ⋅ {1 \over a^{10}} = -{81 \over 5 a^{10}}\)

(Uitdelen)
\(f(x) = {x^{7} \over 2 x^{4}} + {3 x \over 2 x^{4}} = \frac{1}{2} x^{3} + \frac{3}{2} x^{-3}\)

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

(Herleiden)
\(f'(x) = 1\frac{1}{2} x^{2} - {9 \over 2 x^{4}}\)

(Herleiden)
\(f(a) = {7 \over 8 \sqrt{a}} + 2 \sqrt{a} = \frac{7}{8} a^{-\frac{1}{2}} + 2 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{7}{8} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 2 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{7 \over 16 a \sqrt{a}} + {1 \over \sqrt{a}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 8 ⋅ (\frac{7}{8} a + 6)^{7} ⋅ \frac{7}{8}\)

(Herleiden)
\(f'(a) = 14 (\frac{7}{8} a + 6)^{7} \text{.}\)

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

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

(Herleiden)
\(f'(p) = 24 ⋅ (2 p + 5)^{-5} = {24 \over (2 p + 5)^{5}}\)

(Herleiden)
\(f(x) = -\frac{3}{4} \sqrt{5 x - 3} = -\frac{3}{4} ⋅ (5 x - 3)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(x) = -\frac{15}{8} ⋅ (5 x - 3)^{-\frac{1}{2}} = -{15 \over 8 \sqrt{5 x - 3}}\)

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

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

(Herleiden)
\(f'(x) = -\frac{9}{10} ⋅ (3 x + 1)^{-1\frac{1}{2}} = -{9 \over 10 (3 x + 1) \sqrt{3 x + 1}}\)