Differentieer.
2p
\(f(x) = 6 x^{2} + 9 x\)
○
\(f'(x) = 6 ⋅ 2 ⋅ x^{1} + 9 \text{.}\)
1p
○
\(f'(x) = 12 x + 9 \text{.}\)
1p
Differentieer.
2p
\(f(x) = 3 x^{9} - 7 x^{8} + 9 x^{5} - 6 x^{4}\)
○
\(f'(x) = 3 ⋅ 9 ⋅ x^{8} - 7 ⋅ 8 ⋅ x^{7} + 9 ⋅ 5 ⋅ x^{4} - 6 ⋅ 4 ⋅ x^{3} \text{.}\)
1p
○
\(f'(x) = 27 x^{8} - 56 x^{7} + 45 x^{4} - 24 x^{3} \text{.}\)
1p
Differentieer.
2p
\(f(x) = \frac{1}{7} x^{9} + \frac{2}{3} x^{6} + 1\frac{4}{5} x^{4}\)
○
\(f'(x) = \frac{1}{7} ⋅ 9 ⋅ x^{8} + \frac{2}{3} ⋅ 6 ⋅ x^{5} + 1\frac{4}{5} ⋅ 4 ⋅ x^{3} \text{.}\)
1p
○
\(f'(x) = 1\frac{2}{7} x^{8} + 4 x^{5} + 7\frac{1}{5} x^{3} \text{.}\)
1p
Differentieer.
2p
\(f(x) = (4 x^{5} - 2) (x + 9)\)
○
(Haakjes wegwerken)
\(f(x) = (4 x^{5} - 2) (x + 9) = 4 x^{6} + 36 x^{5} - 2 x - 18\)
1p
○
(Differentiëren)
\(f'(x) = 24 x^{5} + 180 x^{4} - 2 \text{.}\)
1p
Differentieer.
2p
\(f(a) = (3 a^{2} - 5)^{2}\)
○
(Haakjes wegwerken)
\(f(a) = (3 a^{2} - 5)^{2} = 9 a^{4} - 30 a^{2} + 25\)
1p
○
(Differentiëren)
\(f'(a) = 36 a^{3} - 60 a \text{.}\)
1p
Differentieer.
3p
\(f(p) = 6 p ⋅ \sqrt[7]{p^{2}}\)
○
(Herleiden)
\(f(p) = 6 p ⋅ \sqrt[7]{p^{2}} = 6 ⋅ p^{1} ⋅ p^{\frac{2}{7}} = 6 ⋅ p^{1\frac{2}{7}}\)
1p
○
(Differentiëren)
\(f'(p) = 6 ⋅ 1\frac{2}{7} ⋅ p^{\frac{2}{7}}\)
1p
○
(Herleiden)
\(f'(p) = 7\frac{5}{7} ⋅ p^{0} ⋅ p^{\frac{2}{7}} = 7\frac{5}{7} ⋅ \sqrt[7]{p^{2}}\)
1p
Differentieer.
3p
\(f(p) = {2 \over 5 p^{8}}\)
○
(Herleiden)
\(f(p) = {2 \over 5 p^{8}} = \frac{2}{5} p^{-8}\)
1p
○
(Differentiëren)
\(f'(p) = \frac{2}{5} ⋅ -8 ⋅ p^{-9} = -\frac{16}{5} ⋅ p^{-9}\)
1p
○
(Herleiden)
\(f'(p) = -\frac{16}{5} ⋅ {1 \over p^{9}} = -{16 \over 5 p^{9}}\)
1p
Differentieer.
3p
\(f(p) = {2 \over 3 \sqrt{p}} + 4 \sqrt{p}\)
○
(Herleiden)
\(f(p) = {2 \over 3 \sqrt{p}} + 4 \sqrt{p} = \frac{2}{3} p^{-\frac{1}{2}} + 4 p^{\frac{1}{2}}\)
1p
○
(Differentiëren)
\(f'(p) = \frac{2}{3} ⋅ -\frac{1}{2} ⋅ p^{-1\frac{1}{2}} + 4 ⋅ \frac{1}{2} ⋅ p^{-\frac{1}{2}}\)
1p
○
(Herleiden)
\(f'(p) = -{1 \over 3 p \sqrt{p}} + {2 \over \sqrt{p}}\)
1p
Differentieer.
3p
\(f(a) = {a^{6} - 4 a^{2} \over 3 a^{3}}\)
○
(Uitdelen)
\(f(a) = {a^{6} \over 3 a^{3}} - {4 a^{2} \over 3 a^{3}} = \frac{1}{3} a^{3} - \frac{4}{3} a^{-1}\)
1p
○
(Differentiëren)
\(f'(a) = \frac{1}{3} ⋅ 3 ⋅ a^{2} - \frac{4}{3} ⋅ -1 ⋅ a^{-2}\)
1p
○
(Herleiden)
\(f'(a) = a^{2} + {4 \over 3 a^{2}}\)
1p
Differentieer.
4p
\(f(x) = {3 x^{2} - 5 \over \sqrt[4]{x}}\)
○
(Herleiden)
\(f(x) = {3 x^{2} - 5 \over x^{\frac{1}{4}}}\)
1p
○
(Uitdelen)
\(f(x) = {3 x^{2} \over x^{\frac{1}{4}}} - {5 \over x^{\frac{1}{4}}} = 3 x^{1\frac{3}{4}} - 5 x^{-\frac{1}{4}}\)
1p
○
(Differentiëren)
\(f'(x) = 3 ⋅ 1\frac{3}{4} ⋅ x^{\frac{3}{4}} - 5 ⋅ -\frac{1}{4} ⋅ x^{-1\frac{1}{4}}\)
1p
○
(Herleiden)
\(f'(x) = 5\frac{1}{4} ⋅ \sqrt[4]{x^{3}} + {5 \over 4 x ⋅ \sqrt[4]{x}}\)
1p
Differentieer.
4p
\(f(x) = {4 x - 2 \over x ⋅ \sqrt{x}}\)
○
(Herleiden)
\(f(x) = {4 x - 2 \over x^{1\frac{1}{2}}}\)
1p
○
(Uitdelen)
\(f(x) = {4 x \over x^{1\frac{1}{2}}} - {2 \over x^{1\frac{1}{2}}} = 4 x^{-\frac{1}{2}} - 2 x^{-1\frac{1}{2}}\)
1p
○
(Differentiëren)
\(f'(x) = 4 ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 2 ⋅ -1\frac{1}{2} ⋅ x^{-2\frac{1}{2}}\)
1p
○
(Herleiden)
\(f'(x) = -{2 \over x ⋅ \sqrt{x}} + {3 \over x^{2} ⋅ \sqrt{x}}\)
1p
Differentieer met behulp van de productregel.
2p
\(f(x) = (6 x + 2) (-7 x^{2} + 7 x)\)
○
(Productregel)
\(f'(x) = 6 (-7 x^{2} + 7 x) + (6 x + 2) (-14 x + 7) \text{.}\)
2p
Differentieer met behulp van de productregel.
2p
\(f(x) = (2 x^{2} - 4 x) (6 x^{2} - 5 x + 8)\)
○
(Productregel)
\(f'(x) = (4 x - 4) (6 x^{2} - 5 x + 8) + (2 x^{2} - 4 x) (12 x - 5) \text{.}\)
2p
Differentieer.
2p
\(f(x) = {6 x - 7 \over 5 x - 6}\)
○
(Quotiëntregel)
\(f'(x) = {(5 x - 6) ⋅ 6 - (6 x - 7) ⋅ 5 \over (5 x - 6)^{2}} \text{.}\)
1p
○
\(f'(x) = {(30 x - 36) - (30 x - 35) \over (5 x - 6)^{2}} = {-1 \over (5 x - 6)^{2}} \text{.}\)
1p
Differentieer.
2p
\(f(a) = {4 a^{2} \over 2 a - 8}\)
○
(Quotiëntregel)
\(f'(a) = {(2 a - 8) ⋅ 8 a - 4 a^{2} ⋅ 2 \over (2 a - 8)^{2}} \text{.}\)
1p
○
\(f'(a) = {(16 a^{2} - 64 a) - 8 a^{2} \over (2 a - 8)^{2}} = {8 a^{2} - 64 a \over (2 a - 8)^{2}} \text{.}\)
1p
Differentieer.
2p
\(f(x) = 4 (6 x - 1)^{8}\)
○
(Kettingregel)
\(f'(x) = 4 ⋅ 8 ⋅ (6 x - 1)^{7} ⋅ 6\)
1p
○
(Herleiden)
\(f'(x) = 192 (6 x - 1)^{7} \text{.}\)
1p
Differentieer.
2p
\(f(a) = 6 (2 a^{2} + 3 a + 1)^{4}\)
○
(Kettingregel)
\(f'(a) = 6 ⋅ 4 ⋅ (2 a^{2} + 3 a + 1)^{3} ⋅ (4 a + 3)\)
1p
○
(Herleiden)
\(f'(a) = (96 a + 72) ⋅ (2 a^{2} + 3 a + 1)^{3}\)
1p
Differentieer.
3p
\(f(x) = -{5 \over (3 x + 1)^{2}}\)
○
(Herleiden)
\(f(x) = -{5 \over (3 x + 1)^{2}} = -5 ⋅ (3 x + 1)^{-2}\)
1p
○
(Kettingregel)
\(f'(x) = -5 ⋅ -2 ⋅ (3 x + 1)^{-3} ⋅ 3\)
1p
○
(Herleiden)
\(f'(x) = 30 ⋅ (3 x + 1)^{-3} = {30 \over (3 x + 1)^{3}}\)
1p
Differentieer.
3p
\(f(p) = -\frac{2}{3} \sqrt{2 p + 3}\)
○
(Herleiden)
\(f(p) = -\frac{2}{3} \sqrt{2 p + 3} = -\frac{2}{3} ⋅ (2 p + 3)^{\frac{1}{2}} \text{.}\)
1p
○
(Kettingregel)
\(f'(p) = -\frac{2}{3} ⋅ \frac{1}{2} ⋅ (2 p + 3)^{-\frac{1}{2}} ⋅ 2\)
1p
○
(Herleiden)
\(f'(p) = -\frac{2}{3} ⋅ (2 p + 3)^{-\frac{1}{2}} = -{2 \over 3 \sqrt{2 p + 3}}\)
1p
Differentieer.
3p
\(f(p) = -{2 \over 7 \sqrt{4 p + 2}}\)
○
(Herleiden)
\(f(p) = -{2 \over 7 \sqrt{4 p + 2}} = -\frac{2}{7} ⋅ (4 p + 2)^{-\frac{1}{2}}\)
1p
○
(Kettingregel)
\(f'(p) = -\frac{2}{7} ⋅ -\frac{1}{2} ⋅ (4 p + 2)^{-1\frac{1}{2}} ⋅ 4\)
1p
○
(Herleiden)
\(f'(p) = \frac{4}{7} ⋅ (4 p + 2)^{-1\frac{1}{2}} = {4 \over 7 (4 p + 2) \sqrt{4 p + 2}}\)
1p
Differentieer.
2p
\(f(x) = -2 ⋅ 3^{-6 x^{3} + 4 x^{2}}\)
○
\(f(x) = -2 ⋅ 3^{-6 x^{3} + 4 x^{2}} ⋅ \ln(3) ⋅ (-18 x^{2} + 8 x) = (36 x^{2} - 16 x) ⋅ 3^{-6 x^{3} + 4 x^{2}} ⋅ \ln(3)\)
2p
Differentieer.
2p
\(f(x) = (3 x^{3} + 5 x^{2}) ⋅ e^{3 x - 4}\)
○
\(f(x) = (9 x^{2} + 10 x) ⋅ e^{3 x - 4} + (3 x^{3} + 5 x^{2}) ⋅ e^{3 x - 4} ⋅ 3\)
\(\text{ } = (9 x^{2} + 10 x) ⋅ e^{3 x - 4} + (9 x^{3} + 15 x^{2}) ⋅ e^{3 x - 4}\)
\(\text{ } = (9 x^{3} + 24 x^{2} + 10 x) ⋅ e^{3 x - 4}\)
2p