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

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

\(f'(p) = 4 ⋅ 8 ⋅ p^{7} - 8 ⋅ 4 ⋅ p^{3} - 3 \text{.}\)

\(f'(p) = 32 p^{7} - 32 p^{3} - 3 \text{.}\)

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

\(f'(a) = 8 a^{3} + 1\frac{1}{2} a^{2} \text{.}\)

(Haakjes wegwerken)
\(f(x) = (2 x^{5} + 1) (x + 4) = 2 x^{6} + 8 x^{5} + x + 4\)

(Differentiëren)
\(f'(x) = 12 x^{5} + 40 x^{4} + 1 \text{.}\)

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

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

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

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

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

(Herleiden)
\(f(a) = -7 a^{3} ⋅ \sqrt[3]{a^{2}} = -7 ⋅ a^{3} ⋅ a^{\frac{2}{3}} = -7 ⋅ a^{3\frac{2}{3}}\)

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

(Herleiden)
\(f'(a) = -25\frac{2}{3} ⋅ a^{2} ⋅ a^{\frac{2}{3}} = -25\frac{2}{3} a^{2} ⋅ \sqrt[3]{a^{2}}\)

(Uitdelen)
\(f(a) = {a^{6} \over 2 a^{4}} - {3 a^{3} \over 2 a^{4}} = \frac{1}{2} a^{2} - \frac{3}{2} a^{-1}\)

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

(Herleiden)
\(f'(a) = a + {3 \over 2 a^{2}}\)

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

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

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

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

(Herleiden)
\(f(p) = {9 \over 4 \sqrt{p}} + 3 \sqrt{p} = \frac{9}{4} p^{-\frac{1}{2}} + 3 p^{\frac{1}{2}}\)

(Differentiëren)
\(f'(p) = \frac{9}{4} ⋅ -\frac{1}{2} ⋅ p^{-1\frac{1}{2}} + 3 ⋅ \frac{1}{2} ⋅ p^{-\frac{1}{2}}\)

(Herleiden)
\(f'(p) = -{9 \over 8 p \sqrt{p}} + {3 \over 2 \sqrt{p}}\)

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

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

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

(Herleiden)
\(f'(a) = -{15 \over 2 a^{2} ⋅ \sqrt{a}} - {5 \over 2 a^{3} ⋅ \sqrt{a}}\)

(Kettingregel)
\(f'(x) = 6 ⋅ 7 ⋅ (\frac{8}{9} x + 4)^{6} ⋅ \frac{8}{9}\)

(Herleiden)
\(f'(x) = 37\frac{1}{3} (\frac{8}{9} x + 4)^{6} \text{.}\)

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

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

(Herleiden)
\(f'(a) = 24 ⋅ (3 a - 5)^{-5} = {24 \over (3 a - 5)^{5}}\)

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

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

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

(Herleiden)
\(f(x) = -{5 \over 6 \sqrt{3 x - 4}} = -\frac{5}{6} ⋅ (3 x - 4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x) = -\frac{5}{6} ⋅ -\frac{1}{2} ⋅ (3 x - 4)^{-1\frac{1}{2}} ⋅ 3\)

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