\(f'(p) = 6 ⋅ 3 ⋅ p^{2} + 9 \text{.}\)

\(f'(p) = 18 p^{2} + 9 \text{.}\)

\(f'(a) = 9 ⋅ 6 ⋅ a^{5} + 2 ⋅ 2 ⋅ a^{1} - 3 \text{.}\)

\(f'(a) = 54 a^{5} + 4 a - 3 \text{.}\)

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

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

(Haakjes wegwerken)
\(f(a) = (4 a^{2} - 9) (a + 8) = 4 a^{3} + 32 a^{2} - 9 a - 72\)

(Differentiëren)
\(f'(a) = 12 a^{2} + 64 a - 9 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{5} - 2)^{2} = 16 x^{10} - 16 x^{5} + 4\)

(Differentiëren)
\(f'(x) = 160 x^{9} - 80 x^{4} \text{.}\)

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

(Differentiëren)
\(f'(x) = \frac{3}{2} ⋅ -4 ⋅ x^{-5} = -6 ⋅ x^{-5}\)

(Herleiden)
\(f'(x) = -6 ⋅ {1 \over x^{5}} = -{6 \over x^{5}}\)

(Herleiden)
\(f(p) = -6 p ⋅ \sqrt[8]{p^{7}} = -6 ⋅ p^{1} ⋅ p^{\frac{7}{8}} = -6 ⋅ p^{1\frac{7}{8}}\)

(Differentiëren)
\(f'(p) = -6 ⋅ 1\frac{7}{8} ⋅ p^{\frac{7}{8}}\)

(Herleiden)
\(f'(p) = -11\frac{1}{4} ⋅ p^{0} ⋅ p^{\frac{7}{8}} = -11\frac{1}{4} ⋅ \sqrt[8]{p^{7}}\)

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

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

(Herleiden)
\(f'(a) = a + {6 \over a^{4}}\)

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

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

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

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

(Herleiden)
\(f(a) = {5 \over 9 \sqrt{a}} + 6 \sqrt{a} = \frac{5}{9} a^{-\frac{1}{2}} + 6 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{5}{9} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 6 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{5 \over 18 a \sqrt{a}} + {3 \over \sqrt{a}}\)

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

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

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

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

(Kettingregel)
\(f'(p) = 8 ⋅ 3 ⋅ (2 p - 4)^{2} ⋅ 2\)

(Herleiden)
\(f'(p) = 48 (2 p - 4)^{2} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -24 ⋅ (4 x + 5)^{-3} = -{24 \over (4 x + 5)^{3}}\)

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

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

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

(Herleiden)
\(f(x) = {9 \over 4 \sqrt{3 x + 2}} = \frac{9}{4} ⋅ (3 x + 2)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = \frac{9}{4} ⋅ -\frac{1}{2} ⋅ (3 x + 2)^{-1\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(x) = -\frac{27}{8} ⋅ (3 x + 2)^{-1\frac{1}{2}} = -{27 \over 8 (3 x + 2) \sqrt{3 x + 2}}\)