\(f'(x) = 2 ⋅ x^{1} + 5 \text{.}\)

\(f'(x) = 2 x + 5 \text{.}\)

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

\(f'(a) = 56 a^{6} - 4 a^{3} - 24 a^{2} \text{.}\)

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

\(f'(x) = 22\frac{1}{2} x^{4} + 8 x + 2\frac{2}{3} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (2 a^{3} - 9) (a + 6) = 2 a^{4} + 12 a^{3} - 9 a - 54\)

(Differentiëren)
\(f'(a) = 8 a^{3} + 36 a^{2} - 9 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (2 p^{4} + 5)^{2} = 4 p^{8} + 20 p^{4} + 25\)

(Differentiëren)
\(f'(p) = 32 p^{7} + 80 p^{3} \text{.}\)

(Herleiden)
\(f(a) = -{9 \over 2 a^{3}} = -\frac{9}{2} a^{-3}\)

(Differentiëren)
\(f'(a) = -\frac{9}{2} ⋅ -3 ⋅ a^{-4} = \frac{27}{2} ⋅ a^{-4}\)

(Herleiden)
\(f'(a) = \frac{27}{2} ⋅ {1 \over a^{4}} = {27 \over 2 a^{4}}\)

(Uitdelen)
\(f(a) = {a^{7} \over 3 a^{5}} - {5 a^{3} \over 3 a^{5}} = \frac{1}{3} a^{2} - \frac{5}{3} a^{-2}\)

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

(Herleiden)
\(f'(a) = \frac{2}{3} a + {10 \over 3 a^{3}}\)

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

(Differentiëren)
\(f'(p) = \frac{9}{4} ⋅ -\frac{1}{2} ⋅ p^{-1\frac{1}{2}} - 9 ⋅ \frac{1}{2} ⋅ p^{-\frac{1}{2}}\)

(Herleiden)
\(f'(p) = -{9 \over 8 p \sqrt{p}} - {9 \over 2 \sqrt{p}}\)

(Kettingregel)
\(f'(x) = 8 ⋅ 3 ⋅ (9 x - 5)^{2} ⋅ 9\)

(Herleiden)
\(f'(x) = 216 (9 x - 5)^{2} \text{.}\)

(Herleiden)
\(f(a) = -{5 \over (3 a - 1)^{4}} = -5 ⋅ (3 a - 1)^{-4}\)

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

(Herleiden)
\(f'(a) = 60 ⋅ (3 a - 1)^{-5} = {60 \over (3 a - 1)^{5}}\)

(Herleiden)
\(f(p) = -\frac{7}{9} \sqrt{5 p + 4} = -\frac{7}{9} ⋅ (5 p + 4)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(p) = -\frac{7}{9} ⋅ \frac{1}{2} ⋅ (5 p + 4)^{-\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(p) = -\frac{35}{18} ⋅ (5 p + 4)^{-\frac{1}{2}} = -{35 \over 18 \sqrt{5 p + 4}}\)

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

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

(Herleiden)
\(f'(a) = \frac{6}{7} ⋅ (3 a - 4)^{-1\frac{1}{2}} = {6 \over 7 (3 a - 4) \sqrt{3 a - 4}}\)