\(f'(a) = 5 ⋅ 3 ⋅ a^{2} + 7 \text{.}\)

\(f'(a) = 15 a^{2} + 7 \text{.}\)

\(f'(a) = -4 ⋅ 4 ⋅ a^{3} - 3 ⋅ 2 ⋅ a^{1} - 7 \text{.}\)

\(f'(a) = -16 a^{3} - 6 a - 7 \text{.}\)

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

\(f'(x) = 18 x^{7} + 1\frac{1}{5} x + \frac{1}{2} \text{.}\)

(Haakjes wegwerken)
\(f(p) = (5 p^{3} + 8) (p + 6) = 5 p^{4} + 30 p^{3} + 8 p + 48\)

(Differentiëren)
\(f'(p) = 20 p^{3} + 90 p^{2} + 8 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (3 x^{5} + 1)^{2} = 9 x^{10} + 6 x^{5} + 1\)

(Differentiëren)
\(f'(x) = 90 x^{9} + 30 x^{4} \text{.}\)

(Herleiden)
\(f(a) = -{7 \over 9 a^{6}} = -\frac{7}{9} a^{-6}\)

(Differentiëren)
\(f'(a) = -\frac{7}{9} ⋅ -6 ⋅ a^{-7} = \frac{14}{3} ⋅ a^{-7}\)

(Herleiden)
\(f'(a) = \frac{14}{3} ⋅ {1 \over a^{7}} = {14 \over 3 a^{7}}\)

(Herleiden)
\(f(p) = 5 p ⋅ \sqrt[9]{p^{5}} = 5 ⋅ p^{1} ⋅ p^{\frac{5}{9}} = 5 ⋅ p^{1\frac{5}{9}}\)

(Differentiëren)
\(f'(p) = 5 ⋅ 1\frac{5}{9} ⋅ p^{\frac{5}{9}}\)

(Herleiden)
\(f'(p) = 7\frac{7}{9} ⋅ p^{0} ⋅ p^{\frac{5}{9}} = 7\frac{7}{9} ⋅ \sqrt[9]{p^{5}}\)

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

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

(Herleiden)
\(f'(x) = \frac{2}{5} x + {6 \over 5 x^{3}}\)

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

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

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

(Herleiden)
\(f'(x) = 11\frac{1}{5} x ⋅ \sqrt[5]{x^{4}} - {2 \over 5 x ⋅ \sqrt[5]{x}}\)

(Herleiden)
\(f(a) = {3 \over 7 \sqrt{a}} + 8 \sqrt{a} = \frac{3}{7} a^{-\frac{1}{2}} + 8 a^{\frac{1}{2}}\)

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

(Herleiden)
\(f'(a) = -{3 \over 14 a \sqrt{a}} + {4 \over \sqrt{a}}\)

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

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

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

(Herleiden)
\(f'(a) = -{25 \over 2 a^{3} ⋅ \sqrt{a}} + {7 \over a^{4} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(a) = 3 ⋅ 9 ⋅ (\frac{3}{4} a + 7)^{8} ⋅ \frac{3}{4}\)

(Herleiden)
\(f'(a) = 20\frac{1}{4} (\frac{3}{4} a + 7)^{8} \text{.}\)

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

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

(Herleiden)
\(f'(x) = 60 ⋅ (4 x - 1)^{-6} = {60 \over (4 x - 1)^{6}}\)

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

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

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

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

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

(Herleiden)
\(f'(a) = \frac{10}{7} ⋅ (4 a + 2)^{-1\frac{1}{2}} = {10 \over 7 (4 a + 2) \sqrt{4 a + 2}}\)