\(f'(a) = 2 ⋅ a^{1} + 8 \text{.}\)

\(f'(a) = 2 a + 8 \text{.}\)

\(f'(x) = -6 ⋅ 8 ⋅ x^{7} + 3 ⋅ 2 ⋅ x^{1} \text{.}\)

\(f'(x) = -48 x^{7} + 6 x \text{.}\)

\(f'(a) = \frac{1}{3} ⋅ 9 ⋅ a^{8} + \frac{5}{6} ⋅ 5 ⋅ a^{4} + \frac{4}{7} \text{.}\)

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

(Haakjes wegwerken)
\(f(p) = (7 p^{2} - 8) (p - 4) = 7 p^{3} - 28 p^{2} - 8 p + 32\)

(Differentiëren)
\(f'(p) = 21 p^{2} - 56 p - 8 \text{.}\)

(Haakjes wegwerken)
\(f(x) = (3 x^{4} + 5)^{2} = 9 x^{8} + 30 x^{4} + 25\)

(Differentiëren)
\(f'(x) = 72 x^{7} + 120 x^{3} \text{.}\)

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

(Differentiëren)
\(f'(p) = \frac{8}{3} ⋅ -2 ⋅ p^{-3} = -\frac{16}{3} ⋅ p^{-3}\)

(Herleiden)
\(f'(p) = -\frac{16}{3} ⋅ {1 \over p^{3}} = -{16 \over 3 p^{3}}\)

(Kettingregel)
\(f'(x) = 4 ⋅ 7 ⋅ (5 x - 2)^{6} ⋅ 5\)

(Herleiden)
\(f'(x) = 140 (5 x - 2)^{6} \text{.}\)

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

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

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

(Herleiden)
\(f(a) = -5 \sqrt{4 a - 3} = -5 ⋅ (4 a - 3)^{\frac{1}{2}} \text{.}\)

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

(Herleiden)
\(f'(a) = -10 ⋅ (4 a - 3)^{-\frac{1}{2}} = -{10 \over \sqrt{4 a - 3}}\)

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

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

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

(Herleiden)
\(f(p) = -8 p ⋅ \sqrt[9]{p^{5}} = -8 ⋅ p^{1} ⋅ p^{\frac{5}{9}} = -8 ⋅ p^{1\frac{5}{9}}\)

(Differentiëren)
\(f'(p) = -8 ⋅ 1\frac{5}{9} ⋅ p^{\frac{5}{9}}\)

(Herleiden)
\(f'(p) = -12\frac{4}{9} ⋅ p^{0} ⋅ p^{\frac{5}{9}} = -12\frac{4}{9} ⋅ \sqrt[9]{p^{5}}\)

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

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

(Herleiden)
\(f'(x) = -{9 \over 4 x \sqrt{x}} - {2 \over \sqrt{x}}\)

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

(Herleiden)
\(f'(a) = (90 a^{2} + 180 a + 60) ⋅ (a^{3} + 3 a^{2} + 2 a)^{4}\)

\(f(p) = -4 ⋅ 2^{-3 p^{2} + 5 p} ⋅ \ln(2) ⋅ (-6 p + 5) = (24 p - 20) ⋅ 2^{-3 p^{2} + 5 p} ⋅ \ln(2)\)

(Quotiëntregel)
\(f'(a) = {(-3 a - 9) ⋅ 3 - (3 a + 7) ⋅ -3 \over (-3 a - 9)^{2}} \text{.}\)

\(f'(a) = {(-9 a - 27) - (-9 a - 21) \over (-3 a - 9)^{2}} = {-6 \over (-3 a - 9)^{2}} \text{.}\)

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

\(f'(x) = {(30 x^{2} - 18 x) - 15 x^{2} \over (-5 x + 3)^{2}} = {15 x^{2} - 18 x \over (-5 x + 3)^{2}} \text{.}\)