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

\(f'(x) = 12 x + 1 \text{.}\)

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

\(f'(p) = 24 p^{7} + 49 p^{6} - 2 p \text{.}\)

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

\(f'(a) = 14 a^{6} + 6 a^{3} + 1\frac{7}{9} a \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{3} + 8) (x - 9) = 4 x^{4} - 36 x^{3} + 8 x - 72\)

(Differentiëren)
\(f'(x) = 16 x^{3} - 108 x^{2} + 8 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (3 a^{4} + 5)^{2} = 9 a^{8} + 30 a^{4} + 25\)

(Differentiëren)
\(f'(a) = 72 a^{7} + 120 a^{3} \text{.}\)

(Herleiden)
\(f(x) = -{7 \over 6 x^{9}} = -\frac{7}{6} x^{-9}\)

(Differentiëren)
\(f'(x) = -\frac{7}{6} ⋅ -9 ⋅ x^{-10} = \frac{21}{2} ⋅ x^{-10}\)

(Herleiden)
\(f'(x) = \frac{21}{2} ⋅ {1 \over x^{10}} = {21 \over 2 x^{10}}\)

(Herleiden)
\(f(p) = -9 p^{3} ⋅ \sqrt[7]{p^{6}} = -9 ⋅ p^{3} ⋅ p^{\frac{6}{7}} = -9 ⋅ p^{3\frac{6}{7}}\)

(Differentiëren)
\(f'(p) = -9 ⋅ 3\frac{6}{7} ⋅ p^{2\frac{6}{7}}\)

(Herleiden)
\(f'(p) = -34\frac{5}{7} ⋅ p^{2} ⋅ p^{\frac{6}{7}} = -34\frac{5}{7} p^{2} ⋅ \sqrt[7]{p^{6}}\)

(Uitdelen)
\(f(a) = {a^{6} \over 2 a^{3}} + {3 a^{2} \over 2 a^{3}} = \frac{1}{2} a^{3} + \frac{3}{2} a^{-1}\)

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

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

(Herleiden)
\(f(x) = {4 x^{3} + 1 \over x^{\frac{1}{5}}}\)

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

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

(Herleiden)
\(f'(x) = 11\frac{1}{5} x ⋅ \sqrt[5]{x^{4}} - {1 \over 5 x ⋅ \sqrt[5]{x}}\)

(Herleiden)
\(f(a) = {9 \over 2 \sqrt{a}} - 7 \sqrt{a} = \frac{9}{2} a^{-\frac{1}{2}} - 7 a^{\frac{1}{2}}\)

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

(Herleiden)
\(f'(a) = -{9 \over 4 a \sqrt{a}} - {7 \over 2 \sqrt{a}}\)

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

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

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

(Herleiden)
\(f'(p) = {6 \over p^{2} ⋅ \sqrt{p}} - {15 \over 2 p^{3} ⋅ \sqrt{p}}\)

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

(Herleiden)
\(f'(x) = 12 (x + 5)^{2} \text{.}\)

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

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

(Herleiden)
\(f'(p) = -40 ⋅ (4 p - 3)^{-6} = -{40 \over (4 p - 3)^{6}}\)

(Herleiden)
\(f(x) = -4 \sqrt{2 x - 5} = -4 ⋅ (2 x - 5)^{\frac{1}{2}} \text{.}\)

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

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

(Herleiden)
\(f(a) = -{2 \over 9 \sqrt{2 a - 3}} = -\frac{2}{9} ⋅ (2 a - 3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{2}{9} ⋅ -\frac{1}{2} ⋅ (2 a - 3)^{-1\frac{1}{2}} ⋅ 2\)

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