\(f'(a) = 5 ⋅ 2 ⋅ a^{1} \text{.}\)

\(f'(a) = 10 a \text{.}\)

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

\(f'(a) = -63 a^{8} - 16 a^{7} + 25 a^{4} \text{.}\)

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

\(f'(x) = 24 x^{7} + \frac{1}{5} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{4} + 7) (x + 6) = 5 x^{5} + 30 x^{4} + 7 x + 42\)

(Differentiëren)
\(f'(x) = 25 x^{4} + 120 x^{3} + 7 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (5 p^{3} - 1)^{2} = 25 p^{6} - 10 p^{3} + 1\)

(Differentiëren)
\(f'(p) = 150 p^{5} - 30 p^{2} \text{.}\)

(Productregel)
\(f'(x) = -9 (-7 x^{2} + 4 x) + (-9 x - 4) (-14 x + 4) \text{.}\)

(Productregel)
\(f'(a) = (2 a + 6) (5 a^{2} - 5 a - 7) + (a^{2} + 6 a) (10 a - 5) \text{.}\)

(Quotiëntregel)
\(f'(p) = {(-3 p - 5) ⋅ 9 - (9 p + 6) ⋅ -3 \over (-3 p - 5)^{2}} \text{.}\)

\(f'(p) = {(-27 p - 45) - (-27 p - 18) \over (-3 p - 5)^{2}} = {-27 \over (-3 p - 5)^{2}} \text{.}\)

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

\(f'(x) = {(10 x^{2} - 6 x) - 5 x^{2} \over (5 x - 3)^{2}} = {5 x^{2} - 6 x \over (5 x - 3)^{2}} \text{.}\)

(Herleiden)
\(f(a) = {7 \over 6 a^{4}} = \frac{7}{6} a^{-4}\)

(Differentiëren)
\(f'(a) = \frac{7}{6} ⋅ -4 ⋅ a^{-5} = -\frac{14}{3} ⋅ a^{-5}\)

(Herleiden)
\(f'(a) = -\frac{14}{3} ⋅ {1 \over a^{5}} = -{14 \over 3 a^{5}}\)

(Herleiden)
\(f(a) = 2 a ⋅ \sqrt[7]{a^{6}} = 2 ⋅ a^{1} ⋅ a^{\frac{6}{7}} = 2 ⋅ a^{1\frac{6}{7}}\)

(Differentiëren)
\(f'(a) = 2 ⋅ 1\frac{6}{7} ⋅ a^{\frac{6}{7}}\)

(Herleiden)
\(f'(a) = 3\frac{5}{7} ⋅ a^{0} ⋅ a^{\frac{6}{7}} = 3\frac{5}{7} ⋅ \sqrt[7]{a^{6}}\)

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

(Differentiëren)
\(f'(p) = \frac{1}{5} ⋅ 2 ⋅ p + \frac{4}{5} ⋅ -3 ⋅ p^{-4}\)

(Herleiden)
\(f'(p) = \frac{2}{5} p - {12 \over 5 p^{4}}\)

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

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

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

(Herleiden)
\(f'(x) = 18\frac{2}{3} x^{3} ⋅ \sqrt[3]{x^{2}} - {1 \over 3 x ⋅ \sqrt[3]{x}}\)

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

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

(Herleiden)
\(f'(x) = -{5 \over 12 x \sqrt{x}} + {1 \over \sqrt{x}}\)

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

(Uitdelen)
\(f(p) = {-5 p \over p^{1\frac{1}{2}}} - {2 \over p^{1\frac{1}{2}}} = -5 p^{-\frac{1}{2}} - 2 p^{-1\frac{1}{2}}\)

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

(Herleiden)
\(f'(p) = {5 \over 2 p ⋅ \sqrt{p}} + {3 \over p^{2} ⋅ \sqrt{p}}\)

(Kettingregel)
\(f'(x) = 9 ⋅ 3 ⋅ (8 x + 5)^{2} ⋅ 8\)

(Herleiden)
\(f'(x) = 216 (8 x + 5)^{2} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -30 ⋅ (3 x - 1)^{-3} = -{30 \over (3 x - 1)^{3}}\)

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

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

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

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

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

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

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

(Herleiden)
\(f'(p) = (144 p^{2} + 144 p + 120) ⋅ (2 p^{3} + 3 p^{2} + 5 p)^{5}\)

\(f(x) = -4 ⋅ e^{-5 x + 1} + (-4 x + 1) ⋅ e^{-5 x + 1} ⋅ -5\)
\(\text{ } = -4 ⋅ e^{-5 x + 1} + (20 x - 5) ⋅ e^{-5 x + 1}\)
\(\text{ } = (20 x - 9) ⋅ e^{-5 x + 1}\)

\(f(x) = 5 ⋅ e^{-3 x - 2} ⋅ -3 = -15 ⋅ e^{-3 x - 2}\)