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

\(f'(a) = 8 a + 7 \text{.}\)

\(f'(x) = 8 ⋅ 5 ⋅ x^{4} - 3 ⋅ 3 ⋅ x^{2} - 2 \text{.}\)

\(f'(x) = 40 x^{4} - 9 x^{2} - 2 \text{.}\)

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

\(f'(p) = 24 p^{8} + 6\frac{1}{4} p^{4} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (8 x^{3} - 4) (x - 7) = 8 x^{4} - 56 x^{3} - 4 x + 28\)

(Differentiëren)
\(f'(x) = 32 x^{3} - 168 x^{2} - 4 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (2 a^{4} + 3)^{2} = 4 a^{8} + 12 a^{4} + 9\)

(Differentiëren)
\(f'(a) = 32 a^{7} + 48 a^{3} \text{.}\)

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

(Differentiëren)
\(f'(x) = \frac{7}{9} ⋅ -7 ⋅ x^{-8} = -\frac{49}{9} ⋅ x^{-8}\)

(Herleiden)
\(f'(x) = -\frac{49}{9} ⋅ {1 \over x^{8}} = -{49 \over 9 x^{8}}\)

(Herleiden)
\(f(p) = 4 p^{2} ⋅ \sqrt[7]{p^{6}} = 4 ⋅ p^{2} ⋅ p^{\frac{6}{7}} = 4 ⋅ p^{2\frac{6}{7}}\)

(Differentiëren)
\(f'(p) = 4 ⋅ 2\frac{6}{7} ⋅ p^{1\frac{6}{7}}\)

(Herleiden)
\(f'(p) = 11\frac{3}{7} ⋅ p^{1} ⋅ p^{\frac{6}{7}} = 11\frac{3}{7} p ⋅ \sqrt[7]{p^{6}}\)

(Uitdelen)
\(f(a) = {a^{6} \over 3 a^{4}} + {2 a \over 3 a^{4}} = \frac{1}{3} a^{2} + \frac{2}{3} a^{-3}\)

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

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

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

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

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

(Herleiden)
\(f'(a) = 11\frac{1}{5} a ⋅ \sqrt[5]{a^{4}} + {2 \over 5 a ⋅ \sqrt[5]{a}}\)

(Herleiden)
\(f(x) = {6 \over 7 \sqrt{x}} - 3 \sqrt{x} = \frac{6}{7} x^{-\frac{1}{2}} - 3 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{6}{7} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 3 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{3 \over 7 x \sqrt{x}} - {3 \over 2 \sqrt{x}}\)

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

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

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

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

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

(Herleiden)
\(f'(a) = 72 (4 a + 5)^{5} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -24 ⋅ (2 x + 1)^{-4} = -{24 \over (2 x + 1)^{4}}\)

(Herleiden)
\(f(a) = -\frac{3}{4} \sqrt{5 a + 3} = -\frac{3}{4} ⋅ (5 a + 3)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(a) = -\frac{15}{8} ⋅ (5 a + 3)^{-\frac{1}{2}} = -{15 \over 8 \sqrt{5 a + 3}}\)

(Herleiden)
\(f(x) = -{2 \over 7 \sqrt{3 x + 5}} = -\frac{2}{7} ⋅ (3 x + 5)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = -\frac{2}{7} ⋅ -\frac{1}{2} ⋅ (3 x + 5)^{-1\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(x) = \frac{3}{7} ⋅ (3 x + 5)^{-1\frac{1}{2}} = {3 \over 7 (3 x + 5) \sqrt{3 x + 5}}\)