Differentiëren

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

\(f'(a) = 18 a^{2} + 3 \text{.}\)

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

\(f'(x) = 54 x^{5} - 6 x^{2} + 5 \text{.}\)

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

\(f'(a) = 40 a^{7} + 9 a^{5} + 1\frac{1}{8} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (3 a^{4} - 8) (a - 9) = 3 a^{5} - 27 a^{4} - 8 a + 72\)

(Differentiëren)
\(f'(a) = 15 a^{4} - 108 a^{3} - 8 \text{.}\)

(Haakjes wegwerken)
\(f(a) = (4 a^{5} - 3)^{2} = 16 a^{10} - 24 a^{5} + 9\)

(Differentiëren)
\(f'(a) = 160 a^{9} - 120 a^{4} \text{.}\)

(Herleiden)
\(f(p) = 7 p ⋅ \sqrt[9]{p^{2}} = 7 ⋅ p^{1} ⋅ p^{\frac{2}{9}} = 7 ⋅ p^{1\frac{2}{9}}\)

(Differentiëren)
\(f'(p) = 7 ⋅ 1\frac{2}{9} ⋅ p^{\frac{2}{9}}\)

(Herleiden)
\(f'(p) = 8\frac{5}{9} ⋅ p^{0} ⋅ p^{\frac{2}{9}} = 8\frac{5}{9} ⋅ \sqrt[9]{p^{2}}\)

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

(Differentiëren)
\(f'(x) = \frac{4}{3} ⋅ -4 ⋅ x^{-5} = -\frac{16}{3} ⋅ x^{-5}\)

(Herleiden)
\(f'(x) = -\frac{16}{3} ⋅ {1 \over x^{5}} = -{16 \over 3 x^{5}}\)

(Herleiden)
\(f(a) = {7 \over 8 \sqrt{a}} - 3 \sqrt{a} = \frac{7}{8} a^{-\frac{1}{2}} - 3 a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a) = \frac{7}{8} ⋅ -\frac{1}{2} ⋅ a^{-1\frac{1}{2}} - 3 ⋅ \frac{1}{2} ⋅ a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a) = -{7 \over 16 a \sqrt{a}} - {3 \over 2 \sqrt{a}}\)

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

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

(Herleiden)
\(f'(a) = \frac{2}{3} a - {2 \over a^{4}}\)

(Herleiden)
\(f(a) = {5 a^{4} + 2 \over a^{\frac{1}{3}}}\)

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

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

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

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

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

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

(Herleiden)
\(f'(a) = {25 \over 2 a^{3} ⋅ \sqrt{a}} - {14 \over a^{4} ⋅ \sqrt{a}}\)

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

(Productregel)
\(f'(a) = (14 a - 2) (8 a^{2} - a - 7) + (7 a^{2} - 2 a) (16 a - 1) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(x - 4) ⋅ 6 - (6 x - 7) ⋅ 1 \over (x - 4)^{2}} \text{.}\)

\(f'(x) = {(6 x - 24) - (6 x - 7) \over (x - 4)^{2}} = {-17 \over (x - 4)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(2 a - 1) ⋅ 16 a - 8 a^{2} ⋅ 2 \over (2 a - 1)^{2}} \text{.}\)

\(f'(a) = {(32 a^{2} - 16 a) - 16 a^{2} \over (2 a - 1)^{2}} = {16 a^{2} - 16 a \over (2 a - 1)^{2}} \text{.}\)

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

(Herleiden)
\(f'(a) = 240 (6 a - 4)^{4} \text{.}\)

(Kettingregel)
\(f'(x) = 3 ⋅ 4 ⋅ (5 x^{4} + 2 x^{2} + 6 x)^{3} ⋅ (20 x^{3} + 4 x + 6)\)

(Herleiden)
\(f'(x) = (240 x^{3} + 48 x + 72) ⋅ (5 x^{4} + 2 x^{2} + 6 x)^{3}\)

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

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

(Herleiden)
\(f'(p) = 24 ⋅ (2 p + 1)^{-4} = {24 \over (2 p + 1)^{4}}\)

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

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

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

(Herleiden)
\(f(a) = -{3 \over 7 \sqrt{3 a + 5}} = -\frac{3}{7} ⋅ (3 a + 5)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{3}{7} ⋅ -\frac{1}{2} ⋅ (3 a + 5)^{-1\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(a) = \frac{9}{14} ⋅ (3 a + 5)^{-1\frac{1}{2}} = {9 \over 14 (3 a + 5) \sqrt{3 a + 5}}\)

\(f(a) = 5 ⋅ 3^{-2 a^{2} - a} ⋅ \ln(3) ⋅ (-4 a - 1) = (-20 a - 5) ⋅ 3^{-2 a^{2} - a} ⋅ \ln(3)\)

\(f(a) = 10 a ⋅ e^{2 a + 3} + (5 a^{2} - 4) ⋅ e^{2 a + 3} ⋅ 2\)
\(\text{ } = 10 a ⋅ e^{2 a + 3} + (10 a^{2} - 8) ⋅ e^{2 a + 3}\)
\(\text{ } = (10 a^{2} + 10 a - 8) ⋅ e^{2 a + 3}\)