\(f'(x) = 5 ⋅ 2 ⋅ x^{1} + 6 \text{.}\)

\(f'(x) = 10 x + 6 \text{.}\)

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

\(f'(a) = 12 a^{5} + 16 a - 3 \text{.}\)

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

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

(Haakjes wegwerken)
\(f(a) = (3 a^{5} - 6) (a - 2) = 3 a^{6} - 6 a^{5} - 6 a + 12\)

(Differentiëren)
\(f'(a) = 18 a^{5} - 30 a^{4} - 6 \text{.}\)

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

(Differentiëren)
\(f'(x) = 96 x^{5} + 48 x^{2} \text{.}\)

(Herleiden)
\(f(x) = {2 \over 5 x^{7}} = \frac{2}{5} x^{-7}\)

(Differentiëren)
\(f'(x) = \frac{2}{5} ⋅ -7 ⋅ x^{-8} = -\frac{14}{5} ⋅ x^{-8}\)

(Herleiden)
\(f'(x) = -\frac{14}{5} ⋅ {1 \over x^{8}} = -{14 \over 5 x^{8}}\)

(Herleiden)
\(f(p) = -9 p ⋅ \sqrt[7]{p^{2}} = -9 ⋅ p^{1} ⋅ p^{\frac{2}{7}} = -9 ⋅ p^{1\frac{2}{7}}\)

(Differentiëren)
\(f'(p) = -9 ⋅ 1\frac{2}{7} ⋅ p^{\frac{2}{7}}\)

(Herleiden)
\(f'(p) = -11\frac{4}{7} ⋅ p^{0} ⋅ p^{\frac{2}{7}} = -11\frac{4}{7} ⋅ \sqrt[7]{p^{2}}\)

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

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

(Herleiden)
\(f'(a) = \frac{1}{2} a + {5 \over 2 a^{3}}\)

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

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

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

(Herleiden)
\(f'(x) = 5\frac{3}{5} x ⋅ \sqrt[5]{x^{4}} + {1 \over 5 x ⋅ \sqrt[5]{x}}\)

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

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

(Herleiden)
\(f'(a) = -{2 \over 3 a \sqrt{a}} - {2 \over \sqrt{a}}\)

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

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

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

(Herleiden)
\(f'(x) = {10 \over x^{3} ⋅ \sqrt{x}} + {7 \over x^{4} ⋅ \sqrt{x}}\)

(Kettingregel)
\(f'(x) = 7 ⋅ 5 ⋅ (x - 6)^{4} ⋅ 1\)

(Herleiden)
\(f'(x) = 35 (x - 6)^{4} \text{.}\)

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

(Kettingregel)
\(f'(p) = -3 ⋅ -5 ⋅ (2 p - 4)^{-6} ⋅ 2\)

(Herleiden)
\(f'(p) = 30 ⋅ (2 p - 4)^{-6} = {30 \over (2 p - 4)^{6}}\)

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

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

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

(Herleiden)
\(f(a) = {8 \over 7 \sqrt{4 a + 1}} = \frac{8}{7} ⋅ (4 a + 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = \frac{8}{7} ⋅ -\frac{1}{2} ⋅ (4 a + 1)^{-1\frac{1}{2}} ⋅ 4\)

(Herleiden)
\(f'(a) = -\frac{16}{7} ⋅ (4 a + 1)^{-1\frac{1}{2}} = -{16 \over 7 (4 a + 1) \sqrt{4 a + 1}}\)