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

\(f'(x) = 21 x^{2} + 4 \text{.}\)

\(f'(p) = -4 ⋅ 8 ⋅ p^{7} + 6 ⋅ 7 ⋅ p^{6} + 3 ⋅ 5 ⋅ p^{4} \text{.}\)

\(f'(p) = -32 p^{7} + 42 p^{6} + 15 p^{4} \text{.}\)

\(f'(x) = 1\frac{1}{4} ⋅ 9 ⋅ x^{8} + \frac{6}{7} ⋅ 6 ⋅ x^{5} + \frac{8}{9} ⋅ 5 ⋅ x^{4} + \frac{2}{3} ⋅ 2 ⋅ x^{1} \text{.}\)

\(f'(x) = 11\frac{1}{4} x^{8} + 5\frac{1}{7} x^{5} + 4\frac{4}{9} x^{4} + 1\frac{1}{3} x \text{.}\)

(Haakjes wegwerken)
\(f(a) = (5 a^{2} + 6) (a - 1) = 5 a^{3} - 5 a^{2} + 6 a - 6\)

(Differentiëren)
\(f'(a) = 15 a^{2} - 10 a + 6 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (3 a^{2} + 5)^{2} = 9 a^{4} + 30 a^{2} + 25\)

(Differentiëren)
\(f'(a) = 36 a^{3} + 60 a \text{.}\)

(Herleiden)
\(f(x) = {9 \over 5 x^{4}} = \frac{9}{5} x^{-4}\)

(Differentiëren)
\(f'(x) = \frac{9}{5} ⋅ -4 ⋅ x^{-5} = -\frac{36}{5} ⋅ x^{-5}\)

(Herleiden)
\(f'(x) = -\frac{36}{5} ⋅ {1 \over x^{5}} = -{36 \over 5 x^{5}}\)

(Kettingregel)
\(f'(a) = 2 ⋅ 6 ⋅ (\frac{3}{5} a - 8)^{5} ⋅ \frac{3}{5}\)

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

(Herleiden)
\(f(p) = {3 \over (2 p - 1)^{5}} = 3 ⋅ (2 p - 1)^{-5}\)

(Kettingregel)
\(f'(p) = 3 ⋅ -5 ⋅ (2 p - 1)^{-6} ⋅ 2\)

(Herleiden)
\(f'(p) = -30 ⋅ (2 p - 1)^{-6} = -{30 \over (2 p - 1)^{6}}\)

(Herleiden)
\(f(x) = -\frac{2}{9} \sqrt{5 x - 4} = -\frac{2}{9} ⋅ (5 x - 4)^{\frac{1}{2}} \text{.}\)

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

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

(Herleiden)
\(f(a) = -{9 \over 8 \sqrt{5 a - 1}} = -\frac{9}{8} ⋅ (5 a - 1)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{9}{8} ⋅ -\frac{1}{2} ⋅ (5 a - 1)^{-1\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(a) = \frac{45}{16} ⋅ (5 a - 1)^{-1\frac{1}{2}} = {45 \over 16 (5 a - 1) \sqrt{5 a - 1}}\)

(Herleiden)
\(f(p) = 8 p ⋅ \sqrt[7]{p^{2}} = 8 ⋅ p^{1} ⋅ p^{\frac{2}{7}} = 8 ⋅ p^{1\frac{2}{7}}\)

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

(Herleiden)
\(f'(p) = 10\frac{2}{7} ⋅ p^{0} ⋅ p^{\frac{2}{7}} = 10\frac{2}{7} ⋅ \sqrt[7]{p^{2}}\)

(Herleiden)
\(f(a) = {8 \over 3 \sqrt{a}} - 6 \sqrt{a} = \frac{8}{3} a^{-\frac{1}{2}} - 6 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{8}{3} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} - 6 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{4 \over 3 a \sqrt{a}} - {3 \over \sqrt{a}}\)

(Kettingregel)
\(f'(x) = 5 ⋅ 4 ⋅ (3 x^{4} + 6 x^{3} + 2 x^{2})^{3} ⋅ (12 x^{3} + 18 x^{2} + 4 x)\)

(Herleiden)
\(f'(x) = (240 x^{3} + 360 x^{2} + 80 x) ⋅ (3 x^{4} + 6 x^{3} + 2 x^{2})^{3}\)

\(f(a) = 4 ⋅ e^{2 a + 3} ⋅ 2 = 8 ⋅ e^{2 a + 3}\)

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

\(f'(p) = {(-18 p - 6) - (-18 p - 9) \over (-3 p - 1)^{2}} = {3 \over (-3 p - 1)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(4 x - 7) ⋅ 12 x - 6 x^{2} ⋅ 4 \over (4 x - 7)^{2}} \text{.}\)

\(f'(x) = {(48 x^{2} - 84 x) - 24 x^{2} \over (4 x - 7)^{2}} = {24 x^{2} - 84 x \over (4 x - 7)^{2}} \text{.}\)