Differentiëren

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

\(f'(a) = 12 a^{2} + 9 \text{.}\)

\(f'(a) = -2 ⋅ 7 ⋅ a^{6} + 6 ⋅ 3 ⋅ a^{2} - 5 ⋅ 2 ⋅ a^{1} - 4 \text{.}\)

\(f'(a) = -14 a^{6} + 18 a^{2} - 10 a - 4 \text{.}\)

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

\(f'(p) = 6 p^{8} + 2\frac{1}{4} p + \frac{1}{5} \text{.}\)

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

(Differentiëren)
\(f'(x) = 18 x^{2} - 12 x - 3 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{5} + 2)^{2} = 16 x^{10} + 16 x^{5} + 4\)

(Differentiëren)
\(f'(x) = 160 x^{9} + 80 x^{4} \text{.}\)

(Herleiden)
\(f(p) = 6 p^{2} ⋅ \sqrt[8]{p^{5}} = 6 ⋅ p^{2} ⋅ p^{\frac{5}{8}} = 6 ⋅ p^{2\frac{5}{8}}\)

(Differentiëren)
\(f'(p) = 6 ⋅ 2\frac{5}{8} ⋅ p^{1\frac{5}{8}}\)

(Herleiden)
\(f'(p) = 15\frac{3}{4} ⋅ p^{1} ⋅ p^{\frac{5}{8}} = 15\frac{3}{4} p ⋅ \sqrt[8]{p^{5}}\)

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

(Differentiëren)
\(f'(a) = -\frac{7}{2} ⋅ -3 ⋅ a^{-4} = \frac{21}{2} ⋅ a^{-4}\)

(Herleiden)
\(f'(a) = \frac{21}{2} ⋅ {1 \over a^{4}} = {21 \over 2 a^{4}}\)

(Herleiden)
\(f(a) = {6 \over 5 \sqrt{a}} + 7 \sqrt{a} = \frac{6}{5} a^{-\frac{1}{2}} + 7 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{6}{5} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} + 7 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{3 \over 5 a \sqrt{a}} + {7 \over 2 \sqrt{a}}\)

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

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

(Herleiden)
\(f'(x) = \frac{2}{3} x + {4 \over 3 x^{2}}\)

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

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

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

(Herleiden)
\(f'(x) = 11\frac{1}{5} x ⋅ \sqrt[5]{x^{4}} + {1 \over 5 x ⋅ \sqrt[5]{x}}\)

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

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

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

(Herleiden)
\(f'(a) = {1 \over a ⋅ \sqrt{a}} + {15 \over 2 a^{2} ⋅ \sqrt{a}}\)

(Quotiëntregel)
\(f'(x) = {(-4 x - 1) ⋅ -3 - (-3 x - 8) ⋅ -4 \over (-4 x - 1)^{2}} \text{.}\)

\(f'(x) = {(12 x + 3) - (12 x + 32) \over (-4 x - 1)^{2}} = {-29 \over (-4 x - 1)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(p) = {(-4 p - 8) ⋅ -12 p - -6 p^{2} ⋅ -4 \over (-4 p - 8)^{2}} \text{.}\)

\(f'(p) = {(48 p^{2} + 96 p) - 24 p^{2} \over (-4 p - 8)^{2}} = {24 p^{2} + 96 p \over (-4 p - 8)^{2}} \text{.}\)

(Kettingregel)
\(f'(a) = 6 ⋅ 5 ⋅ (9 a - 8)^{4} ⋅ 9\)

(Herleiden)
\(f'(a) = 270 (9 a - 8)^{4} \text{.}\)

(Kettingregel)
\(f'(p) = 2 ⋅ 4 ⋅ (6 p^{3} + 5 p^{2} + 3)^{3} ⋅ (18 p^{2} + 10 p)\)

(Herleiden)
\(f'(p) = (144 p^{2} + 80 p) ⋅ (6 p^{3} + 5 p^{2} + 3)^{3}\)

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

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

(Herleiden)
\(f'(x) = 20 ⋅ (4 x + 2)^{-6} = {20 \over (4 x + 2)^{6}}\)

(Herleiden)
\(f(x) = \frac{4}{9} \sqrt{3 x + 2} = \frac{4}{9} ⋅ (3 x + 2)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(x) = \frac{4}{9} ⋅ \frac{1}{2} ⋅ (3 x + 2)^{-\frac{1}{2}} ⋅ 3\)

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

(Herleiden)
\(f(a) = -{3 \over 7 \sqrt{2 a - 3}} = -\frac{3}{7} ⋅ (2 a - 3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{3}{7} ⋅ -\frac{1}{2} ⋅ (2 a - 3)^{-1\frac{1}{2}} ⋅ 2\)

(Herleiden)
\(f'(a) = \frac{3}{7} ⋅ (2 a - 3)^{-1\frac{1}{2}} = {3 \over 7 (2 a - 3) \sqrt{2 a - 3}}\)

\(f(a) = 6 ⋅ e^{-3 a^{3} - 2} ⋅ -9 a^{2} = -54 a^{2} ⋅ e^{-3 a^{3} - 2}\)

\(f(p) = -1 ⋅ e^{3 p - 4} + (-p + 3) ⋅ e^{3 p - 4} ⋅ 3\)
\(\text{ } = -1 ⋅ e^{3 p - 4} + (-3 p + 9) ⋅ e^{3 p - 4}\)
\(\text{ } = (-3 p + 8) ⋅ e^{3 p - 4}\)

(Productregel)
\(f'(a) = 2 (-3 a^{2} + 7 a) + (2 a - 5) (-6 a + 7) \text{.}\)

(Productregel)
\(f'(x) = (12 x - 6) (-2 x^{2} + x - 8) + (6 x^{2} - 6 x) (-4 x + 1) \text{.}\)