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

\(f'(p) = 12 p^{2} + 1 \text{.}\)

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

\(f'(a) = 24 a^{7} + 10 a - 6 \text{.}\)

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

\(f'(a) = 6\frac{3}{7} a^{8} + 10\frac{1}{2} a^{6} + 1\frac{7}{8} a^{4} + \frac{8}{9} a^{3} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (9 x^{2} + 8) (x - 7) = 9 x^{3} - 63 x^{2} + 8 x - 56\)

(Differentiëren)
\(f'(x) = 27 x^{2} - 126 x + 8 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{4} + 1)^{2} = 25 x^{8} + 10 x^{4} + 1\)

(Differentiëren)
\(f'(x) = 200 x^{7} + 40 x^{3} \text{.}\)

(Herleiden)
\(f(x) = -{6 \over 7 x^{2}} = -\frac{6}{7} x^{-2}\)

(Differentiëren)
\(f'(x) = -\frac{6}{7} ⋅ -2 ⋅ x^{-3} = \frac{12}{7} ⋅ x^{-3}\)

(Herleiden)
\(f'(x) = \frac{12}{7} ⋅ {1 \over x^{3}} = {12 \over 7 x^{3}}\)

(Uitdelen)
\(f(a) = {a^{9} \over 5 a^{6}} - {3 a^{3} \over 5 a^{6}} = \frac{1}{5} a^{3} - \frac{3}{5} a^{-3}\)

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

(Herleiden)
\(f'(a) = \frac{3}{5} a^{2} + {9 \over 5 a^{4}}\)

(Herleiden)
\(f(a) = {7 \over 8 \sqrt{a}} - 5 \sqrt{a} = \frac{7}{8} a^{-\frac{1}{2}} - 5 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{7}{8} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} - 5 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{7 \over 16 a \sqrt{a}} - {5 \over 2 \sqrt{a}}\)

(Kettingregel)
\(f'(a) = 8 ⋅ 4 ⋅ (5 a + 6)^{3} ⋅ 5\)

(Herleiden)
\(f'(a) = 160 (5 a + 6)^{3} \text{.}\)

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

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

(Herleiden)
\(f'(p) = -24 ⋅ (3 p + 1)^{-3} = -{24 \over (3 p + 1)^{3}}\)

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

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

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

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

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

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