\(f'(a) = 3 ⋅ a^{2} + 6 \text{.}\)

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

\(f'(a) = 8 ⋅ 9 ⋅ a^{8} - 1 ⋅ 7 ⋅ a^{6} + 6 \text{.}\)

\(f'(a) = 72 a^{8} - 7 a^{6} + 6 \text{.}\)

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

\(f'(x) = \frac{7}{8} x^{6} + 7 x^{4} + 1\frac{1}{2} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (2 p^{5} + 6) (p - 4) = 2 p^{6} - 8 p^{5} + 6 p - 24\)

(Differentiëren)
\(f'(p) = 12 p^{5} - 40 p^{4} + 6 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{5} - 1)^{2} = 16 x^{10} - 8 x^{5} + 1\)

(Differentiëren)
\(f'(x) = 160 x^{9} - 40 x^{4} \text{.}\)

(Herleiden)
\(f(p) = {7 \over 2 p^{4}} = \frac{7}{2} p^{-4}\)

(Differentiëren)
\(f'(p) = \frac{7}{2} ⋅ -4 ⋅ p^{-5} = -14 ⋅ p^{-5}\)

(Herleiden)
\(f'(p) = -14 ⋅ {1 \over p^{5}} = -{14 \over p^{5}}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 3 ⋅ (6 x + 9)^{2} ⋅ 6\)

(Herleiden)
\(f'(x) = 36 (6 x + 9)^{2} \text{.}\)

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

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

(Herleiden)
\(f'(x) = -20 ⋅ (5 x - 3)^{-5} = -{20 \over (5 x - 3)^{5}}\)

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

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

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

(Herleiden)
\(f(a) = {7 \over 4 \sqrt{5 a + 4}} = \frac{7}{4} ⋅ (5 a + 4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = \frac{7}{4} ⋅ -\frac{1}{2} ⋅ (5 a + 4)^{-1\frac{1}{2}} ⋅ 5\)

(Herleiden)
\(f'(a) = -\frac{35}{8} ⋅ (5 a + 4)^{-1\frac{1}{2}} = -{35 \over 8 (5 a + 4) \sqrt{5 a + 4}}\)

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

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

(Herleiden)
\(f'(x) = 4\frac{4}{5} ⋅ x^{1} ⋅ x^{\frac{2}{5}} = 4\frac{4}{5} x ⋅ \sqrt[5]{x^{2}}\)

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

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

(Herleiden)
\(f'(p) = -{9 \over 14 p \sqrt{p}} - {3 \over 2 \sqrt{p}}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 5 ⋅ (4 x^{4} + x^{2} + 6)^{4} ⋅ (16 x^{3} + 2 x)\)

(Herleiden)
\(f'(x) = (160 x^{3} + 20 x) ⋅ (4 x^{4} + x^{2} + 6)^{4}\)

\(f(p) = 4 ⋅ 2^{3 p - 5} ⋅ \ln(2) ⋅ 3 = 12 ⋅ 2^{3 p - 5} ⋅ \ln(2)\)

(Quotiëntregel)
\(f'(x) = {(2 x + 5) ⋅ -2 - (-2 x + 8) ⋅ 2 \over (2 x + 5)^{2}} \text{.}\)

\(f'(x) = {(-4 x - 10) - (-4 x + 16) \over (2 x + 5)^{2}} = {-26 \over (2 x + 5)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(p) = {(-5 p - 3) ⋅ 12 p - 6 p^{2} ⋅ -5 \over (-5 p - 3)^{2}} \text{.}\)

\(f'(p) = {(-60 p^{2} - 36 p) - -30 p^{2} \over (-5 p - 3)^{2}} = {-30 p^{2} - 36 p \over (-5 p - 3)^{2}} \text{.}\)