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

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

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

\(f'(x) = 25 x^{4} + 16 x^{3} - 12 x \text{.}\)

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

\(f'(a) = 18 a^{7} + 7 a^{4} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (8 a^{2} + 9) (a - 5) = 8 a^{3} - 40 a^{2} + 9 a - 45\)

(Differentiëren)
\(f'(a) = 24 a^{2} - 80 a + 9 \text{.}\)

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

(Differentiëren)
\(f'(p) = 96 p^{5} - 48 p^{2} \text{.}\)

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

(Differentiëren)
\(f'(x) = -\frac{5}{4} ⋅ -3 ⋅ x^{-4} = \frac{15}{4} ⋅ x^{-4}\)

(Herleiden)
\(f'(x) = \frac{15}{4} ⋅ {1 \over x^{4}} = {15 \over 4 x^{4}}\)

(Kettingregel)
\(f'(p) = 5 ⋅ 8 ⋅ (\frac{7}{8} p - 1)^{7} ⋅ \frac{7}{8}\)

(Herleiden)
\(f'(p) = 35 (\frac{7}{8} p - 1)^{7} \text{.}\)

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

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

(Herleiden)
\(f'(a) = -40 ⋅ (5 a - 1)^{-3} = -{40 \over (5 a - 1)^{3}}\)

(Herleiden)
\(f(a) = \frac{6}{7} \sqrt{2 a + 5} = \frac{6}{7} ⋅ (2 a + 5)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(a) = \frac{6}{7} ⋅ \frac{1}{2} ⋅ (2 a + 5)^{-\frac{1}{2}} ⋅ 2\)

(Herleiden)
\(f'(a) = \frac{6}{7} ⋅ (2 a + 5)^{-\frac{1}{2}} = {6 \over 7 \sqrt{2 a + 5}}\)

(Herleiden)
\(f(x) = {8 \over 5 \sqrt{5 x - 3}} = \frac{8}{5} ⋅ (5 x - 3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = \frac{8}{5} ⋅ -\frac{1}{2} ⋅ (5 x - 3)^{-1\frac{1}{2}} ⋅ 5\)

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

(Herleiden)
\(f(a) = 5 a^{3} ⋅ \sqrt[3]{a^{2}} = 5 ⋅ a^{3} ⋅ a^{\frac{2}{3}} = 5 ⋅ a^{3\frac{2}{3}}\)

(Differentiëren)
\(f'(a) = 5 ⋅ 3\frac{2}{3} ⋅ a^{2\frac{2}{3}}\)

(Herleiden)
\(f'(a) = 18\frac{1}{3} ⋅ a^{2} ⋅ a^{\frac{2}{3}} = 18\frac{1}{3} a^{2} ⋅ \sqrt[3]{a^{2}}\)

(Herleiden)
\(f(p) = {8 \over 3 \sqrt{p}} + 8 \sqrt{p} = \frac{8}{3} p^{-\frac{1}{2}} + 8 p^{\frac{1}{2}}\)

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

(Herleiden)
\(f'(p) = -{4 \over 3 p \sqrt{p}} + {4 \over \sqrt{p}}\)

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

(Herleiden)
\(f'(a) = (108 a^{2} + 90) ⋅ (2 a^{3} + 5 a + 1)^{2}\)

\(f(x) = -2 ⋅ e^{5 x^{2} + 3 x} ⋅ (10 x + 3) = (-20 x - 6) ⋅ e^{5 x^{2} + 3 x}\)

(Quotiëntregel)
\(f'(a) = {(7 a + 8) ⋅ -1 - (-a + 4) ⋅ 7 \over (7 a + 8)^{2}} \text{.}\)

\(f'(a) = {(-7 a - 8) - (-7 a + 28) \over (7 a + 8)^{2}} = {-36 \over (7 a + 8)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(x) = {(-2 x + 5) ⋅ 18 x - 9 x^{2} ⋅ -2 \over (-2 x + 5)^{2}} \text{.}\)

\(f'(x) = {(-36 x^{2} + 90 x) - -18 x^{2} \over (-2 x + 5)^{2}} = {-18 x^{2} + 90 x \over (-2 x + 5)^{2}} \text{.}\)