\(f'(x) = 2 ⋅ x^{1} + 3 \text{.}\)

\(f'(x) = 2 x + 3 \text{.}\)

\(f'(x) = -9 ⋅ 2 ⋅ x^{1} + 8 \text{.}\)

\(f'(x) = -18 x + 8 \text{.}\)

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

\(f'(a) = 15 a^{8} + 20 a^{4} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (7 a^{4} - 8) (a + 9) = 7 a^{5} + 63 a^{4} - 8 a - 72\)

(Differentiëren)
\(f'(a) = 35 a^{4} + 252 a^{3} - 8 \text{.}\)

(Haakjes wegwerken)
\(f(p) = (5 p^{4} - 2)^{2} = 25 p^{8} - 20 p^{4} + 4\)

(Differentiëren)
\(f'(p) = 200 p^{7} - 80 p^{3} \text{.}\)

(Productregel)
\(f'(a) = -4 (-5 a^{2} - 9 a) + (-4 a + 5) (-10 a - 9) \text{.}\)

(Productregel)
\(f'(p) = (-6 p + 6) (-7 p^{2} - 5 p + 5) + (-3 p^{2} + 6 p) (-14 p - 5) \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-5 x + 4) ⋅ 5 - (5 x - 6) ⋅ -5 \over (-5 x + 4)^{2}} \text{.}\)

\(f'(x) = {(-25 x + 20) - (-25 x + 30) \over (-5 x + 4)^{2}} = {-10 \over (-5 x + 4)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-7 x - 3) ⋅ 14 x - 7 x^{2} ⋅ -7 \over (-7 x - 3)^{2}} \text{.}\)

\(f'(x) = {(-98 x^{2} - 42 x) - -49 x^{2} \over (-7 x - 3)^{2}} = {-49 x^{2} - 42 x \over (-7 x - 3)^{2}} \text{.}\)

(Herleiden)
\(f(a) = -{7 \over 8 a^{7}} = -\frac{7}{8} a^{-7}\)

(Differentiëren)
\(f'(a) = -\frac{7}{8} ⋅ -7 ⋅ a^{-8} = \frac{49}{8} ⋅ a^{-8}\)

(Herleiden)
\(f'(a) = \frac{49}{8} ⋅ {1 \over a^{8}} = {49 \over 8 a^{8}}\)

(Herleiden)
\(f(a) = -5 a^{2} ⋅ \sqrt[7]{a^{5}} = -5 ⋅ a^{2} ⋅ a^{\frac{5}{7}} = -5 ⋅ a^{2\frac{5}{7}}\)

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

(Herleiden)
\(f'(a) = -13\frac{4}{7} ⋅ a^{1} ⋅ a^{\frac{5}{7}} = -13\frac{4}{7} a ⋅ \sqrt[7]{a^{5}}\)

(Uitdelen)
\(f(p) = {p^{6} \over 3 p^{3}} - {4 p \over 3 p^{3}} = \frac{1}{3} p^{3} - \frac{4}{3} p^{-2}\)

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

(Herleiden)
\(f'(p) = p^{2} + {8 \over 3 p^{3}}\)

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

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

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

(Herleiden)
\(f'(x) = 11\frac{2}{5} x^{2} ⋅ \sqrt[5]{x^{4}} + {2 \over 5 x ⋅ \sqrt[5]{x}}\)

(Herleiden)
\(f(x) = {9 \over 7 \sqrt{x}} - 6 \sqrt{x} = \frac{9}{7} x^{-\frac{1}{2}} - 6 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{9}{7} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 6 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{9 \over 14 x \sqrt{x}} - {3 \over \sqrt{x}}\)

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

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

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

(Herleiden)
\(f'(x) = -{2 \over x ⋅ \sqrt{x}} + {9 \over 2 x^{2} ⋅ \sqrt{x}}\)

(Kettingregel)
\(f'(p) = 5 ⋅ 8 ⋅ (6 p + 2)^{7} ⋅ 6\)

(Herleiden)
\(f'(p) = 240 (6 p + 2)^{7} \text{.}\)

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

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

(Herleiden)
\(f'(a) = 24 ⋅ (3 a + 1)^{-3} = {24 \over (3 a + 1)^{3}}\)

(Herleiden)
\(f(x) = -\frac{7}{9} \sqrt{2 x - 3} = -\frac{7}{9} ⋅ (2 x - 3)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(x) = -\frac{7}{9} ⋅ \frac{1}{2} ⋅ (2 x - 3)^{-\frac{1}{2}} ⋅ 2\)

(Herleiden)
\(f'(x) = -\frac{7}{9} ⋅ (2 x - 3)^{-\frac{1}{2}} = -{7 \over 9 \sqrt{2 x - 3}}\)

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

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

(Herleiden)
\(f'(x) = \frac{10}{9} ⋅ (5 x - 4)^{-1\frac{1}{2}} = {10 \over 9 (5 x - 4) \sqrt{5 x - 4}}\)

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

(Herleiden)
\(f'(a) = (96 a^{3} + 40) ⋅ (3 a^{4} + 5 a + 6)^{3}\)

\(f(a) = (-8 a - 1) ⋅ e^{-3 a + 5} + (-4 a^{2} - a) ⋅ e^{-3 a + 5} ⋅ -3\)
\(\text{ } = (-8 a - 1) ⋅ e^{-3 a + 5} + (12 a^{2} + 3 a) ⋅ e^{-3 a + 5}\)
\(\text{ } = (12 a^{2} - 5 a - 1) ⋅ e^{-3 a + 5}\)

\(f(p) = -6 ⋅ 3^{-5 p + 4} ⋅ \ln(3) ⋅ -5 = 30 ⋅ 3^{-5 p + 4} ⋅ \ln(3)\)