\(f'(a) = 3 ⋅ 3 ⋅ a^{2} + 5 \text{.}\)

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

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

\(f'(a) = -81 a^{8} - 12 a^{3} + 3 a^{2} \text{.}\)

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

\(f'(p) = 22\frac{1}{2} p^{4} + 3\frac{1}{5} p \text{.}\)

(Haakjes wegwerken)
\(f(x) = (2 x^{3} - 6) (x - 4) = 2 x^{4} - 8 x^{3} - 6 x + 24\)

(Differentiëren)
\(f'(x) = 8 x^{3} - 24 x^{2} - 6 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{2} - 3)^{2} = 25 x^{4} - 30 x^{2} + 9\)

(Differentiëren)
\(f'(x) = 100 x^{3} - 60 x \text{.}\)

(Herleiden)
\(f(p) = {8 \over 3 p^{7}} = \frac{8}{3} p^{-7}\)

(Differentiëren)
\(f'(p) = \frac{8}{3} ⋅ -7 ⋅ p^{-8} = -\frac{56}{3} ⋅ p^{-8}\)

(Herleiden)
\(f'(p) = -\frac{56}{3} ⋅ {1 \over p^{8}} = -{56 \over 3 p^{8}}\)

(Kettingregel)
\(f'(a) = 9 ⋅ 6 ⋅ (4 a - 2)^{5} ⋅ 4\)

(Herleiden)
\(f'(a) = 216 (4 a - 2)^{5} \text{.}\)

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

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

(Herleiden)
\(f'(x) = 40 ⋅ (5 x + 3)^{-5} = {40 \over (5 x + 3)^{5}}\)

(Herleiden)
\(f(a) = \frac{4}{9} \sqrt{2 a - 5} = \frac{4}{9} ⋅ (2 a - 5)^{\frac{1}{2}} \text{.}\)

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

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

(Herleiden)
\(f(x) = {2 \over 7 \sqrt{2 x + 4}} = \frac{2}{7} ⋅ (2 x + 4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = \frac{2}{7} ⋅ -\frac{1}{2} ⋅ (2 x + 4)^{-1\frac{1}{2}} ⋅ 2\)

(Herleiden)
\(f'(x) = -\frac{2}{7} ⋅ (2 x + 4)^{-1\frac{1}{2}} = -{2 \over 7 (2 x + 4) \sqrt{2 x + 4}}\)

(Herleiden)
\(f(p) = 2 p ⋅ \sqrt[7]{p^{5}} = 2 ⋅ p^{1} ⋅ p^{\frac{5}{7}} = 2 ⋅ p^{1\frac{5}{7}}\)

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

(Herleiden)
\(f'(p) = 3\frac{3}{7} ⋅ p^{0} ⋅ p^{\frac{5}{7}} = 3\frac{3}{7} ⋅ \sqrt[7]{p^{5}}\)

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

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

(Herleiden)
\(f'(x) = -{9 \over 4 x \sqrt{x}} - {3 \over 2 \sqrt{x}}\)

(Kettingregel)
\(f'(a) = 5 ⋅ 6 ⋅ (3 a^{3} + a + 4)^{5} ⋅ (9 a^{2} + 1)\)

(Herleiden)
\(f'(a) = (270 a^{2} + 30) ⋅ (3 a^{3} + a + 4)^{5}\)

\(f(a) = 5 ⋅ 4^{6 a^{3} + 2 a^{2}} ⋅ \ln(4) ⋅ (18 a^{2} + 4 a) = (90 a^{2} + 20 a) ⋅ 4^{6 a^{3} + 2 a^{2}} ⋅ \ln(4)\)

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

\(f'(x) = {(16 x + 6) - (16 x - 64) \over (-8 x - 3)^{2}} = {70 \over (-8 x - 3)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-7 a + 4) ⋅ -16 a - -8 a^{2} ⋅ -7 \over (-7 a + 4)^{2}} \text{.}\)

\(f'(a) = {(112 a^{2} - 64 a) - 56 a^{2} \over (-7 a + 4)^{2}} = {56 a^{2} - 64 a \over (-7 a + 4)^{2}} \text{.}\)