\(f'(a) = 6 ⋅ 2 ⋅ a^{1} + 9 \text{.}\)

\(f'(a) = 12 a + 9 \text{.}\)

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

\(f'(x) = -48 x^{7} + 12 x^{3} - 14 x \text{.}\)

\(f'(a) = 1\frac{4}{5} ⋅ 9 ⋅ a^{8} + \frac{6}{7} ⋅ 5 ⋅ a^{4} + \frac{1}{2} \text{.}\)

\(f'(a) = 16\frac{1}{5} a^{8} + 4\frac{2}{7} a^{4} + \frac{1}{2} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (9 p^{3} - 5) (p + 1) = 9 p^{4} + 9 p^{3} - 5 p - 5\)

(Differentiëren)
\(f'(p) = 36 p^{3} + 27 p^{2} - 5 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{3} - 1)^{2} = 16 x^{6} - 8 x^{3} + 1\)

(Differentiëren)
\(f'(x) = 96 x^{5} - 24 x^{2} \text{.}\)

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

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

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

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

(Herleiden)
\(f'(p) = 15 (\frac{3}{4} p + 1)^{4} \text{.}\)

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

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

(Herleiden)
\(f'(x) = 40 ⋅ (4 x - 1)^{-3} = {40 \over (4 x - 1)^{3}}\)

(Herleiden)
\(f(a) = \frac{7}{8} \sqrt{3 a - 4} = \frac{7}{8} ⋅ (3 a - 4)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(a) = \frac{7}{8} ⋅ \frac{1}{2} ⋅ (3 a - 4)^{-\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(a) = \frac{21}{16} ⋅ (3 a - 4)^{-\frac{1}{2}} = {21 \over 16 \sqrt{3 a - 4}}\)

(Herleiden)
\(f(a) = -{7 \over 5 \sqrt{3 a + 4}} = -\frac{7}{5} ⋅ (3 a + 4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = -\frac{7}{5} ⋅ -\frac{1}{2} ⋅ (3 a + 4)^{-1\frac{1}{2}} ⋅ 3\)

(Herleiden)
\(f'(a) = \frac{21}{10} ⋅ (3 a + 4)^{-1\frac{1}{2}} = {21 \over 10 (3 a + 4) \sqrt{3 a + 4}}\)

(Herleiden)
\(f(p) = -3 p ⋅ \sqrt[9]{p^{8}} = -3 ⋅ p^{1} ⋅ p^{\frac{8}{9}} = -3 ⋅ p^{1\frac{8}{9}}\)

(Differentiëren)
\(f'(p) = -3 ⋅ 1\frac{8}{9} ⋅ p^{\frac{8}{9}}\)

(Herleiden)
\(f'(p) = -5\frac{2}{3} ⋅ p^{0} ⋅ p^{\frac{8}{9}} = -5\frac{2}{3} ⋅ \sqrt[9]{p^{8}}\)

(Herleiden)
\(f(x) = {5 \over 6 \sqrt{x}} - 5 \sqrt{x} = \frac{5}{6} x^{-\frac{1}{2}} - 5 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{5}{6} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 5 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{5 \over 12 x \sqrt{x}} - {5 \over 2 \sqrt{x}}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 5 ⋅ (6 x^{4} + x^{3} + 4 x^{2})^{4} ⋅ (24 x^{3} + 3 x^{2} + 8 x)\)

(Herleiden)
\(f'(x) = (240 x^{3} + 30 x^{2} + 80 x) ⋅ (6 x^{4} + x^{3} + 4 x^{2})^{4}\)

\(f(p) = 4 ⋅ 3^{-2 p^{3} - 5 p} ⋅ \ln(3) ⋅ (-6 p^{2} - 5) = (-24 p^{2} - 20) ⋅ 3^{-2 p^{3} - 5 p} ⋅ \ln(3)\)

(Quotiëntregel)
\(f'(x) = {(3 x + 9) ⋅ -7 - (-7 x + 1) ⋅ 3 \over (3 x + 9)^{2}} \text{.}\)

\(f'(x) = {(-21 x - 63) - (-21 x + 3) \over (3 x + 9)^{2}} = {-66 \over (3 x + 9)^{2}} \text{.}\)

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

\(f'(x) = {(-64 x^{2} - 128 x) - -32 x^{2} \over (-4 x - 8)^{2}} = {-32 x^{2} - 128 x \over (-4 x - 8)^{2}} \text{.}\)