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

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

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

\(f'(a) = -36 a^{8} + 35 a^{4} - 4 a \text{.}\)

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

\(f'(x) = 2\frac{1}{2} x^{4} + 10\frac{2}{3} x^{3} + 1\frac{4}{5} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (6 x^{2} - 4) (x + 3) = 6 x^{3} + 18 x^{2} - 4 x - 12\)

(Differentiëren)
\(f'(x) = 18 x^{2} + 36 x - 4 \text{.}\)

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

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

(Herleiden)
\(f(a) = -{4 \over 7 a^{9}} = -\frac{4}{7} a^{-9}\)

(Differentiëren)
\(f'(a) = -\frac{4}{7} ⋅ -9 ⋅ a^{-10} = \frac{36}{7} ⋅ a^{-10}\)

(Herleiden)
\(f'(a) = \frac{36}{7} ⋅ {1 \over a^{10}} = {36 \over 7 a^{10}}\)

(Kettingregel)
\(f'(p) = 9 ⋅ 3 ⋅ (2 p + 7)^{2} ⋅ 2\)

(Herleiden)
\(f'(p) = 54 (2 p + 7)^{2} \text{.}\)

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

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

(Herleiden)
\(f'(x) = 30 ⋅ (2 x - 4)^{-4} = {30 \over (2 x - 4)^{4}}\)

(Herleiden)
\(f(a) = \frac{7}{9} \sqrt{2 a + 1} = \frac{7}{9} ⋅ (2 a + 1)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(a) = \frac{7}{9} ⋅ (2 a + 1)^{-\frac{1}{2}} = {7 \over 9 \sqrt{2 a + 1}}\)

(Herleiden)
\(f(x) = -{7 \over 8 \sqrt{5 x - 1}} = -\frac{7}{8} ⋅ (5 x - 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = -\frac{7}{8} ⋅ -\frac{1}{2} ⋅ (5 x - 1)^{-1\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(x) = \frac{35}{16} ⋅ (5 x - 1)^{-1\frac{1}{2}} = {35 \over 16 (5 x - 1) \sqrt{5 x - 1}}\)

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

(Differentiëren)
\(f'(x) = -8 ⋅ 2\frac{7}{8} ⋅ x^{1\frac{7}{8}}\)

(Herleiden)
\(f'(x) = -23 ⋅ x^{1} ⋅ x^{\frac{7}{8}} = -23 x ⋅ \sqrt[8]{x^{7}}\)

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

(Differentiëren)
\(f'(p) = \frac{4}{3} ⋅ -\frac{1}{2} ⋅ p^{-1\frac{1}{2}} - 9 ⋅ \frac{1}{2} ⋅ p^{-\frac{1}{2}}\)

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

(Kettingregel)
\(f'(x) = 5 ⋅ 6 ⋅ (4 x^{4} + 3 x^{3} + 1)^{5} ⋅ (16 x^{3} + 9 x^{2})\)

(Herleiden)
\(f'(x) = (480 x^{3} + 270 x^{2}) ⋅ (4 x^{4} + 3 x^{3} + 1)^{5}\)

\(f(a) = 4 ⋅ e^{-a^{2} - 2 a} ⋅ (-2 a - 2) = (-8 a - 8) ⋅ e^{-a^{2} - 2 a}\)

(Quotiëntregel)
\(f'(x) = {(3 x - 5) ⋅ 6 - (6 x - 1) ⋅ 3 \over (3 x - 5)^{2}} \text{.}\)

\(f'(x) = {(18 x - 30) - (18 x - 3) \over (3 x - 5)^{2}} = {-27 \over (3 x - 5)^{2}} \text{.}\)

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

\(f'(p) = {(-12 p^{2} + 6 p) - -6 p^{2} \over (6 p - 3)^{2}} = {-6 p^{2} + 6 p \over (6 p - 3)^{2}} \text{.}\)