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

\(f'(p) = 18 p^{2} + 7 \text{.}\)

\(f'(x) = -9 ⋅ 9 ⋅ x^{8} - 7 ⋅ 8 ⋅ x^{7} + 2 ⋅ 2 ⋅ x^{1} \text{.}\)

\(f'(x) = -81 x^{8} - 56 x^{7} + 4 x \text{.}\)

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

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

(Haakjes wegwerken)
\(f(a) = (7 a^{2} - 9) (a + 8) = 7 a^{3} + 56 a^{2} - 9 a - 72\)

(Differentiëren)
\(f'(a) = 21 a^{2} + 112 a - 9 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{3} + 5)^{2} = 16 x^{6} + 40 x^{3} + 25\)

(Differentiëren)
\(f'(x) = 96 x^{5} + 120 x^{2} \text{.}\)

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

(Differentiëren)
\(f'(p) = \frac{2}{9} ⋅ -4 ⋅ p^{-5} = -\frac{8}{9} ⋅ p^{-5}\)

(Herleiden)
\(f'(p) = -\frac{8}{9} ⋅ {1 \over p^{5}} = -{8 \over 9 p^{5}}\)

(Uitdelen)
\(f(x) = {x^{8} \over 2 x^{5}} - {4 x^{2} \over 2 x^{5}} = \frac{1}{2} x^{3} - \frac{4}{2} x^{-3}\)

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

(Herleiden)
\(f'(x) = 1\frac{1}{2} x^{2} + {6 \over x^{4}}\)

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

(Differentiëren)
\(f'(x) = \frac{4}{7} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} + 7 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{2 \over 7 x \sqrt{x}} + {7 \over 2 \sqrt{x}}\)

(Kettingregel)
\(f'(a) = 8 ⋅ 5 ⋅ (2 a - 3)^{4} ⋅ 2\)

(Herleiden)
\(f'(a) = 80 (2 a - 3)^{4} \text{.}\)

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

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

(Herleiden)
\(f'(a) = -30 ⋅ (2 a + 4)^{-4} = -{30 \over (2 a + 4)^{4}}\)

(Herleiden)
\(f(p) = \frac{3}{7} \sqrt{3 p + 2} = \frac{3}{7} ⋅ (3 p + 2)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(p) = \frac{9}{14} ⋅ (3 p + 2)^{-\frac{1}{2}} = {9 \over 14 \sqrt{3 p + 2}}\)

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

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

(Herleiden)
\(f'(x) = -\frac{25}{4} ⋅ (5 x + 2)^{-1\frac{1}{2}} = -{25 \over 4 (5 x + 2) \sqrt{5 x + 2}}\)