\(f'(p) = 2 ⋅ 2 ⋅ p^{1} \text{.}\)

\(f'(p) = 4 p \text{.}\)

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

\(f'(x) = 49 x^{6} - 12 x^{2} - 3 \text{.}\)

\(f'(a) = \frac{5}{6} ⋅ 5 ⋅ a^{4} + \frac{3}{7} ⋅ 2 ⋅ a^{1} + \frac{1}{8} \text{.}\)

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

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

(Differentiëren)
\(f'(a) = 45 a^{4} + 36 a^{3} + 3 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (4 x^{5} - 3)^{2} = 16 x^{10} - 24 x^{5} + 9\)

(Differentiëren)
\(f'(x) = 160 x^{9} - 120 x^{4} \text{.}\)

(Herleiden)
\(f(x) = {4 \over 5 x^{9}} = \frac{4}{5} x^{-9}\)

(Differentiëren)
\(f'(x) = \frac{4}{5} ⋅ -9 ⋅ x^{-10} = -\frac{36}{5} ⋅ x^{-10}\)

(Herleiden)
\(f'(x) = -\frac{36}{5} ⋅ {1 \over x^{10}} = -{36 \over 5 x^{10}}\)

(Kettingregel)
\(f'(p) = 9 ⋅ 7 ⋅ (5 p - 3)^{6} ⋅ 5\)

(Herleiden)
\(f'(p) = 315 (5 p - 3)^{6} \text{.}\)

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

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

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

(Herleiden)
\(f(x) = -\frac{5}{8} \sqrt{4 x - 5} = -\frac{5}{8} ⋅ (4 x - 5)^{\frac{1}{2}} \text{.}\)

(Kettingregel)
\(f'(x) = -\frac{5}{8} ⋅ \frac{1}{2} ⋅ (4 x - 5)^{-\frac{1}{2}} ⋅ 4\)

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

(Herleiden)
\(f(a) = {9 \over 8 \sqrt{4 a + 2}} = \frac{9}{8} ⋅ (4 a + 2)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = \frac{9}{8} ⋅ -\frac{1}{2} ⋅ (4 a + 2)^{-1\frac{1}{2}} ⋅ 4\)

(Herleiden)
\(f'(a) = -\frac{9}{4} ⋅ (4 a + 2)^{-1\frac{1}{2}} = -{9 \over 4 (4 a + 2) \sqrt{4 a + 2}}\)

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

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

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

(Herleiden)
\(f(x) = {7 \over 5 \sqrt{x}} - 7 \sqrt{x} = \frac{7}{5} x^{-\frac{1}{2}} - 7 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{7}{5} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 7 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{7 \over 10 x \sqrt{x}} - {7 \over 2 \sqrt{x}}\)

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

(Herleiden)
\(f'(x) = (80 x^{3} + 80 x + 120) ⋅ (x^{4} + 2 x^{2} + 6 x)^{4}\)

\(f(p) = -3 ⋅ 5^{p + 2} ⋅ \ln(5) ⋅ 1 = -3 ⋅ 5^{p + 2} ⋅ \ln(5)\)

(Quotiëntregel)
\(f'(a) = {(3 a - 8) ⋅ 1 - (a - 7) ⋅ 3 \over (3 a - 8)^{2}} \text{.}\)

\(f'(a) = {(3 a - 8) - (3 a - 21) \over (3 a - 8)^{2}} = {13 \over (3 a - 8)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(p) = {(6 p + 9) ⋅ -6 p - -3 p^{2} ⋅ 6 \over (6 p + 9)^{2}} \text{.}\)

\(f'(p) = {(-36 p^{2} - 54 p) - -18 p^{2} \over (6 p + 9)^{2}} = {-18 p^{2} - 54 p \over (6 p + 9)^{2}} \text{.}\)