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

\(f'(a) = 18 a^{2} + 3 \text{.}\)

\(f'(x) = -5 ⋅ 7 ⋅ x^{6} + 4 ⋅ x^{3} - 2 \text{.}\)

\(f'(x) = -35 x^{6} + 4 x^{3} - 2 \text{.}\)

\(f'(a) = 9 ⋅ 7 ⋅ a^{6} + \frac{1}{2} ⋅ 5 ⋅ a^{4} + 2 \text{.}\)

\(f'(a) = 63 a^{6} + 2\frac{1}{2} a^{4} + 2 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (9 x^{4} - 3) (x + 2) = 9 x^{5} + 18 x^{4} - 3 x - 6\)

(Differentiëren)
\(f'(x) = 45 x^{4} + 72 x^{3} - 3 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (2 p^{4} + 1)^{2} = 4 p^{8} + 4 p^{4} + 1\)

(Differentiëren)
\(f'(p) = 32 p^{7} + 16 p^{3} \text{.}\)

(Herleiden)
\(f(a) = {9 \over 5 a^{6}} = \frac{9}{5} a^{-6}\)

(Differentiëren)
\(f'(a) = \frac{9}{5} ⋅ -6 ⋅ a^{-7} = -\frac{54}{5} ⋅ a^{-7}\)

(Herleiden)
\(f'(a) = -\frac{54}{5} ⋅ {1 \over a^{7}} = -{54 \over 5 a^{7}}\)

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

(Differentiëren)
\(f'(p) = 6 ⋅ 2\frac{5}{6} ⋅ p^{1\frac{5}{6}}\)

(Herleiden)
\(f'(p) = 17 ⋅ p^{1} ⋅ p^{\frac{5}{6}} = 17 p ⋅ \sqrt[6]{p^{5}}\)

(Uitdelen)
\(f(a) = {a^{7} \over 2 a^{4}} + {5 a^{2} \over 2 a^{4}} = \frac{1}{2} a^{3} + \frac{5}{2} a^{-2}\)

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

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

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

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

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

(Herleiden)
\(f'(x) = 3\frac{4}{5} x^{2} ⋅ \sqrt[5]{x^{4}} - {3 \over 5 x ⋅ \sqrt[5]{x}}\)

(Herleiden)
\(f(x) = {8 \over 3 \sqrt{x}} + 5 \sqrt{x} = \frac{8}{3} x^{-\frac{1}{2}} + 5 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{8}{3} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} + 5 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{4 \over 3 x \sqrt{x}} + {5 \over 2 \sqrt{x}}\)

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

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

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

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

(Kettingregel)
\(f'(x) = 6 ⋅ 4 ⋅ (x + 8)^{3} ⋅ 1\)

(Herleiden)
\(f'(x) = 24 (x + 8)^{3} \text{.}\)

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

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

(Herleiden)
\(f'(a) = -60 ⋅ (4 a - 1)^{-4} = -{60 \over (4 a - 1)^{4}}\)

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

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

(Herleiden)
\(f'(p) = -6 ⋅ (3 p + 1)^{-\frac{1}{2}} = -{6 \over \sqrt{3 p + 1}}\)

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

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

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