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

\(f'(x) = 4 x + 3 \text{.}\)

\(f'(x) = 5 ⋅ 9 ⋅ x^{8} - 3 ⋅ 6 ⋅ x^{5} - 9 ⋅ 4 ⋅ x^{3} + 3 ⋅ x^{2} \text{.}\)

\(f'(x) = 45 x^{8} - 18 x^{5} - 36 x^{3} + 3 x^{2} \text{.}\)

\(f'(a) = 3\frac{1}{2} ⋅ 6 ⋅ a^{5} + \frac{1}{4} ⋅ 5 ⋅ a^{4} + \frac{5}{9} ⋅ 2 ⋅ a^{1} \text{.}\)

\(f'(a) = 21 a^{5} + 1\frac{1}{4} a^{4} + 1\frac{1}{9} a \text{.}\)

(Haakjes wegwerken)
\(f(p) = (9 p^{5} + 2) (p - 7) = 9 p^{6} - 63 p^{5} + 2 p - 14\)

(Differentiëren)
\(f'(p) = 54 p^{5} - 315 p^{4} + 2 \text{.}\)

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

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

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

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

(Herleiden)
\(f'(a) = 7 ⋅ {1 \over a^{3}} = {7 \over a^{3}}\)

(Uitdelen)
\(f(p) = {p^{8} \over 4 p^{6}} + {3 p^{3} \over 4 p^{6}} = \frac{1}{4} p^{2} + \frac{3}{4} p^{-3}\)

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

(Herleiden)
\(f'(p) = \frac{1}{2} p - {9 \over 4 p^{4}}\)

(Herleiden)
\(f(x) = {4 \over 9 \sqrt{x}} - 8 \sqrt{x} = \frac{4}{9} x^{-\frac{1}{2}} - 8 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{4}{9} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 8 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

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

(Kettingregel)
\(f'(p) = 8 ⋅ 6 ⋅ (\frac{4}{5} p + 4)^{5} ⋅ \frac{4}{5}\)

(Herleiden)
\(f'(p) = 38\frac{2}{5} (\frac{4}{5} p + 4)^{5} \text{.}\)

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

(Kettingregel)
\(f'(x) = 2 ⋅ -5 ⋅ (4 x - 1)^{-6} ⋅ 4\)

(Herleiden)
\(f'(x) = -40 ⋅ (4 x - 1)^{-6} = -{40 \over (4 x - 1)^{6}}\)

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

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

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

(Herleiden)
\(f(a) = -{8 \over 9 \sqrt{3 a - 1}} = -\frac{8}{9} ⋅ (3 a - 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{8}{9} ⋅ -\frac{1}{2} ⋅ (3 a - 1)^{-1\frac{1}{2}} ⋅ 3\)

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