\(f'(p) = 7 ⋅ 3 ⋅ p^{2} + 9 \text{.}\)

\(f'(p) = 21 p^{2} + 9 \text{.}\)

\(f'(a) = -5 ⋅ 9 ⋅ a^{8} - 6 ⋅ 4 ⋅ a^{3} \text{.}\)

\(f'(a) = -45 a^{8} - 24 a^{3} \text{.}\)

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

\(f'(x) = 6\frac{1}{4} x^{4} + 18 x^{2} + 2\frac{1}{4} x + 1\frac{1}{2} \text{.}\)

(Haakjes wegwerken)
\(f(a) = (7 a^{2} + 8) (a + 5) = 7 a^{3} + 35 a^{2} + 8 a + 40\)

(Differentiëren)
\(f'(a) = 21 a^{2} + 70 a + 8 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (5 x^{2} - 1)^{2} = 25 x^{4} - 10 x^{2} + 1\)

(Differentiëren)
\(f'(x) = 100 x^{3} - 20 x \text{.}\)

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

(Differentiëren)
\(f'(a) = \frac{3}{5} ⋅ -4 ⋅ a^{-5} = -\frac{12}{5} ⋅ a^{-5}\)

(Herleiden)
\(f'(a) = -\frac{12}{5} ⋅ {1 \over a^{5}} = -{12 \over 5 a^{5}}\)

(Uitdelen)
\(f(x) = {x^{7} \over 4 x^{5}} - {5 x^{3} \over 4 x^{5}} = \frac{1}{4} x^{2} - \frac{5}{4} x^{-2}\)

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

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

(Herleiden)
\(f(x) = {8 \over 7 \sqrt{x}} - 6 \sqrt{x} = \frac{8}{7} x^{-\frac{1}{2}} - 6 x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x) = \frac{8}{7} ⋅ -\frac{1}{2} ⋅ x^{-1\frac{1}{2}} - 6 ⋅ \frac{1}{2} ⋅ x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x) = -{4 \over 7 x \sqrt{x}} - {3 \over \sqrt{x}}\)

(Kettingregel)
\(f'(p) = 6 ⋅ 9 ⋅ (5 p + 4)^{8} ⋅ 5\)

(Herleiden)
\(f'(p) = 270 (5 p + 4)^{8} \text{.}\)

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

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

(Herleiden)
\(f'(a) = 24 ⋅ (4 a + 1)^{-4} = {24 \over (4 a + 1)^{4}}\)

(Herleiden)
\(f(x) = \frac{4}{7} \sqrt{4 x - 5} = \frac{4}{7} ⋅ (4 x - 5)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(x) = \frac{8}{7} ⋅ (4 x - 5)^{-\frac{1}{2}} = {8 \over 7 \sqrt{4 x - 5}}\)

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

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

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