\(f'(p) = 9 ⋅ 2 ⋅ p^{1} \text{.}\)

\(f'(p) = 18 p \text{.}\)

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

\(f'(a) = 16 a^{7} + 4 a^{3} \text{.}\)

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

\(f'(x) = 1\frac{5}{9} x + \frac{1}{4} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (8 x^{5} - 3) (x - 1) = 8 x^{6} - 8 x^{5} - 3 x + 3\)

(Differentiëren)
\(f'(x) = 48 x^{5} - 40 x^{4} - 3 \text{.}\)

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

(Differentiëren)
\(f'(a) = 150 a^{5} - 120 a^{2} \text{.}\)

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

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

(Herleiden)
\(f'(a) = -9 ⋅ {1 \over a^{3}} = -{9 \over a^{3}}\)

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

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

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

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

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

(Herleiden)
\(f'(p) = -{4 \over 7 p \sqrt{p}} - {5 \over 2 \sqrt{p}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 7 ⋅ (\frac{7}{8} a + 1)^{6} ⋅ \frac{7}{8}\)

(Herleiden)
\(f'(a) = 12\frac{1}{4} (\frac{7}{8} a + 1)^{6} \text{.}\)

(Herleiden)
\(f(p) = -{1 \over (5 p - 3)^{2}} = -1 ⋅ (5 p - 3)^{-2}\)

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

(Herleiden)
\(f'(p) = 10 ⋅ (5 p - 3)^{-3} = {10 \over (5 p - 3)^{3}}\)

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

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

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

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

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

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