\(f'(a) = 3 ⋅ a^{2} + 6 \text{.}\)

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

\(f'(x) = -8 ⋅ 5 ⋅ x^{4} + 4 ⋅ 3 ⋅ x^{2} - 7 ⋅ 2 ⋅ x^{1} + 6 \text{.}\)

\(f'(x) = -40 x^{4} + 12 x^{2} - 14 x + 6 \text{.}\)

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

\(f'(x) = 3\frac{3}{5} x^{8} + \frac{1}{4} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (2 a^{4} + 8) (a - 6) = 2 a^{5} - 12 a^{4} + 8 a - 48\)

(Differentiëren)
\(f'(a) = 10 a^{4} - 48 a^{3} + 8 \text{.}\)

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

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

(Productregel)
\(f'(x) = 7 (4 x^{2} - 9 x) + (7 x - 6) (8 x - 9) \text{.}\)

(Productregel)
\(f'(p) = (-2 p + 5) (-5 p^{2} + p - 9) + (-p^{2} + 5 p) (-10 p + 1) \text{.}\)

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

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

(Quotiëntregel)
\(f'(a) = {(-7 a + 4) ⋅ 4 a - 2 a^{2} ⋅ -7 \over (-7 a + 4)^{2}} \text{.}\)

\(f'(a) = {(-28 a^{2} + 16 a) - -14 a^{2} \over (-7 a + 4)^{2}} = {-14 a^{2} + 16 a \over (-7 a + 4)^{2}} \text{.}\)

(Herleiden)
\(f(a) = -{4 \over 5 a^{5}} = -\frac{4}{5} a^{-5}\)

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

(Herleiden)
\(f'(a) = 4 ⋅ {1 \over a^{6}} = {4 \over a^{6}}\)

(Herleiden)
\(f(a) = 8 a^{2} ⋅ \sqrt[8]{a^{3}} = 8 ⋅ a^{2} ⋅ a^{\frac{3}{8}} = 8 ⋅ a^{2\frac{3}{8}}\)

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

(Herleiden)
\(f'(a) = 19 ⋅ a^{1} ⋅ a^{\frac{3}{8}} = 19 a ⋅ \sqrt[8]{a^{3}}\)

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

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

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

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

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

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

(Herleiden)
\(f'(p) = 5\frac{2}{5} ⋅ \sqrt[5]{p^{4}} - {4 \over 5 p ⋅ \sqrt[5]{p}}\)

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

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

(Herleiden)
\(f'(x) = -{3 \over 8 x \sqrt{x}} + {2 \over \sqrt{x}}\)

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

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

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

(Herleiden)
\(f'(p) = -{2 \over p ⋅ \sqrt{p}} - {15 \over 2 p^{2} ⋅ \sqrt{p}}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 9 ⋅ (5 x - 7)^{8} ⋅ 5\)

(Herleiden)
\(f'(x) = 90 (5 x - 7)^{8} \text{.}\)

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

(Kettingregel)
\(f'(x) = -4 ⋅ -5 ⋅ (3 x - 1)^{-6} ⋅ 3\)

(Herleiden)
\(f'(x) = 60 ⋅ (3 x - 1)^{-6} = {60 \over (3 x - 1)^{6}}\)

(Herleiden)
\(f(a) = 4 \sqrt{3 a + 5} = 4 ⋅ (3 a + 5)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(a) = 6 ⋅ (3 a + 5)^{-\frac{1}{2}} = {6 \over \sqrt{3 a + 5}}\)

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

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

(Herleiden)
\(f'(a) = \frac{15}{8} ⋅ (3 a + 1)^{-1\frac{1}{2}} = {15 \over 8 (3 a + 1) \sqrt{3 a + 1}}\)

(Kettingregel)
\(f'(p) = 3 ⋅ 4 ⋅ (2 p^{4} + 5 p^{3} + p)^{3} ⋅ (8 p^{3} + 15 p^{2} + 1)\)

(Herleiden)
\(f'(p) = (96 p^{3} + 180 p^{2} + 12) ⋅ (2 p^{4} + 5 p^{3} + p)^{3}\)

\(f(x) = (9 x^{2} + 2) ⋅ e^{-2 x - 5} + (3 x^{3} + 2 x) ⋅ e^{-2 x - 5} ⋅ -2\)
\(\text{ } = (9 x^{2} + 2) ⋅ e^{-2 x - 5} + (-6 x^{3} - 4 x) ⋅ e^{-2 x - 5}\)
\(\text{ } = (-6 x^{3} + 9 x^{2} - 4 x + 2) ⋅ e^{-2 x - 5}\)

\(f(x) = 4 ⋅ e^{3 x^{3} + 5 x^{2}} ⋅ (9 x^{2} + 10 x) = (36 x^{2} + 40 x) ⋅ e^{3 x^{3} + 5 x^{2}}\)