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

\(f'(x) = 24 x^{2} + 9 \text{.}\)

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

\(f'(p) = -48 p^{7} - 4 p^{3} + 12 p - 4 \text{.}\)

\(f'(a) = \frac{5}{9} ⋅ 9 ⋅ a^{8} + \frac{1}{2} ⋅ 8 ⋅ a^{7} + \frac{3}{4} ⋅ 5 ⋅ a^{4} + 1\frac{1}{3} ⋅ 4 ⋅ a^{3} \text{.}\)

\(f'(a) = 5 a^{8} + 4 a^{7} + 3\frac{3}{4} a^{4} + 5\frac{1}{3} a^{3} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (8 x^{4} + 6) (x - 5) = 8 x^{5} - 40 x^{4} + 6 x - 30\)

(Differentiëren)
\(f'(x) = 40 x^{4} - 160 x^{3} + 6 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (4 a^{2} + 3)^{2} = 16 a^{4} + 24 a^{2} + 9\)

(Differentiëren)
\(f'(a) = 64 a^{3} + 48 a \text{.}\)

(Herleiden)
\(f(p) = {7 \over 3 p^{2}} = \frac{7}{3} p^{-2}\)

(Differentiëren)
\(f'(p) = \frac{7}{3} ⋅ -2 ⋅ p^{-3} = -\frac{14}{3} ⋅ p^{-3}\)

(Herleiden)
\(f'(p) = -\frac{14}{3} ⋅ {1 \over p^{3}} = -{14 \over 3 p^{3}}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 9 ⋅ (\frac{8}{9} x - 7)^{8} ⋅ \frac{8}{9}\)

(Herleiden)
\(f'(x) = 16 (\frac{8}{9} x - 7)^{8} \text{.}\)

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

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

(Herleiden)
\(f'(a) = -24 ⋅ (2 a - 1)^{-5} = -{24 \over (2 a - 1)^{5}}\)

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

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

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

(Herleiden)
\(f(x) = {7 \over 9 \sqrt{4 x + 5}} = \frac{7}{9} ⋅ (4 x + 5)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = \frac{7}{9} ⋅ -\frac{1}{2} ⋅ (4 x + 5)^{-1\frac{1}{2}} ⋅ 4\)

(Herleiden)
\(f'(x) = -\frac{14}{9} ⋅ (4 x + 5)^{-1\frac{1}{2}} = -{14 \over 9 (4 x + 5) \sqrt{4 x + 5}}\)

(Herleiden)
\(f(x) = -7 x^{3} ⋅ \sqrt[8]{x^{7}} = -7 ⋅ x^{3} ⋅ x^{\frac{7}{8}} = -7 ⋅ x^{3\frac{7}{8}}\)

(Differentiëren)
\(f'(x) = -7 ⋅ 3\frac{7}{8} ⋅ x^{2\frac{7}{8}}\)

(Herleiden)
\(f'(x) = -27\frac{1}{8} ⋅ x^{2} ⋅ x^{\frac{7}{8}} = -27\frac{1}{8} x^{2} ⋅ \sqrt[8]{x^{7}}\)

(Herleiden)
\(f(a) = {3 \over 5 \sqrt{a}} - 9 \sqrt{a} = \frac{3}{5} a^{-\frac{1}{2}} - 9 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{3}{5} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} - 9 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{3 \over 10 a \sqrt{a}} - {9 \over 2 \sqrt{a}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 3 ⋅ (6 a^{4} + a^{2} + 5 a)^{2} ⋅ (24 a^{3} + 2 a + 5)\)

(Herleiden)
\(f'(a) = (144 a^{3} + 12 a + 30) ⋅ (6 a^{4} + a^{2} + 5 a)^{2}\)

\(f(a) = 4 ⋅ e^{-2 a^{3} + 5 a} ⋅ (-6 a^{2} + 5) = (-24 a^{2} + 20) ⋅ e^{-2 a^{3} + 5 a}\)

(Quotiëntregel)
\(f'(a) = {(7 a + 3) ⋅ 2 - (2 a + 6) ⋅ 7 \over (7 a + 3)^{2}} \text{.}\)

\(f'(a) = {(14 a + 6) - (14 a + 42) \over (7 a + 3)^{2}} = {-36 \over (7 a + 3)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-7 x - 9) ⋅ 4 x - 2 x^{2} ⋅ -7 \over (-7 x - 9)^{2}} \text{.}\)

\(f'(x) = {(-28 x^{2} - 36 x) - -14 x^{2} \over (-7 x - 9)^{2}} = {-14 x^{2} - 36 x \over (-7 x - 9)^{2}} \text{.}\)