Differentiëren

\(f'(a) = 3 ⋅ a^{2} + 9 \text{.}\)

\(f'(a) = 3 a^{2} + 9 \text{.}\)

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

\(f'(x) = -16 x^{7} + 8 x^{3} \text{.}\)

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

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

(Haakjes wegwerken)
\(f(p) = (2 p^{4} + 9) (p + 6) = 2 p^{5} + 12 p^{4} + 9 p + 54\)

(Differentiëren)
\(f'(p) = 10 p^{4} + 48 p^{3} + 9 \text{.}\)

(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)
\(f(a) = 9 a^{3} ⋅ \sqrt[4]{a^{3}} = 9 ⋅ a^{3} ⋅ a^{\frac{3}{4}} = 9 ⋅ a^{3\frac{3}{4}}\)

(Differentiëren)
\(f'(a) = 9 ⋅ 3\frac{3}{4} ⋅ a^{2\frac{3}{4}}\)

(Herleiden)
\(f'(a) = 33\frac{3}{4} ⋅ a^{2} ⋅ a^{\frac{3}{4}} = 33\frac{3}{4} a^{2} ⋅ \sqrt[4]{a^{3}}\)

(Herleiden)
\(f(x) = -{6 \over 5 x^{3}} = -\frac{6}{5} x^{-3}\)

(Differentiëren)
\(f'(x) = -\frac{6}{5} ⋅ -3 ⋅ x^{-4} = \frac{18}{5} ⋅ x^{-4}\)

(Herleiden)
\(f'(x) = \frac{18}{5} ⋅ {1 \over x^{4}} = {18 \over 5 x^{4}}\)

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

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

(Herleiden)
\(f'(a) = -{1 \over 7 a \sqrt{a}} - {2 \over \sqrt{a}}\)

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

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

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

(Herleiden)
\(f(p) = {p^{5} - 3 \over p^{\frac{1}{4}}}\)

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

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

(Herleiden)
\(f'(p) = 4\frac{3}{4} p^{3} ⋅ \sqrt[4]{p^{3}} + {3 \over 4 p ⋅ \sqrt[4]{p}}\)

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

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

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

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

(Quotiëntregel)
\(f'(x) = {(-7 x - 8) ⋅ -9 - (-9 x - 5) ⋅ -7 \over (-7 x - 8)^{2}} \text{.}\)

\(f'(x) = {(63 x + 72) - (63 x + 35) \over (-7 x - 8)^{2}} = {37 \over (-7 x - 8)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(a) = {(-a + 3) ⋅ 14 a - 7 a^{2} ⋅ -1 \over (-a + 3)^{2}} \text{.}\)

\(f'(a) = {(-14 a^{2} + 42 a) - -7 a^{2} \over (-a + 3)^{2}} = {-7 a^{2} + 42 a \over (-a + 3)^{2}} \text{.}\)

(Kettingregel)
\(f'(p) = 9 ⋅ 6 ⋅ (p - 2)^{5} ⋅ 1\)

(Herleiden)
\(f'(p) = 54 (p - 2)^{5} \text{.}\)

(Kettingregel)
\(f'(x) = 2 ⋅ 5 ⋅ (3 x^{4} + x^{3} + 4)^{4} ⋅ (12 x^{3} + 3 x^{2})\)

(Herleiden)
\(f'(x) = (120 x^{3} + 30 x^{2}) ⋅ (3 x^{4} + x^{3} + 4)^{4}\)

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

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

(Herleiden)
\(f'(a) = 12 ⋅ (4 a - 2)^{-4} = {12 \over (4 a - 2)^{4}}\)

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

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

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

(Herleiden)
\(f(a) = {5 \over 9 \sqrt{3 a - 4}} = \frac{5}{9} ⋅ (3 a - 4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a) = \frac{5}{9} ⋅ -\frac{1}{2} ⋅ (3 a - 4)^{-1\frac{1}{2}} ⋅ 3\)

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

\(f(a) = 3 ⋅ e^{-a^{2} + 4 a} ⋅ (-2 a + 4) = (-6 a + 12) ⋅ e^{-a^{2} + 4 a}\)

\(f(x) = (9 x^{2} + 5) ⋅ e^{4 x + 5} + (3 x^{3} + 5 x) ⋅ e^{4 x + 5} ⋅ 4\)
\(\text{ } = (9 x^{2} + 5) ⋅ e^{4 x + 5} + (12 x^{3} + 20 x) ⋅ e^{4 x + 5}\)
\(\text{ } = (12 x^{3} + 9 x^{2} + 20 x + 5) ⋅ e^{4 x + 5}\)

(Productregel)
\(f'(p) = -2 (4 p^{2} - 9 p) + (-2 p + 7) (8 p - 9) \text{.}\)

(Productregel)
\(f'(a) = (-4 a - 9) (-a^{2} + a + 2) + (-2 a^{2} - 9 a) (-2 a + 1) \text{.}\)