\(f'(a) = 3 ⋅ a^{2} \text{.}\)

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

\(f'(x) = 7 ⋅ 9 ⋅ x^{8} + 4 ⋅ x^{3} + 4 \text{.}\)

\(f'(x) = 63 x^{8} + 4 x^{3} + 4 \text{.}\)

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

\(f'(x) = 2 x^{5} + 9 x^{2} + 2\frac{1}{2} x \text{.}\)

(Haakjes wegwerken)
\(f(p) = (8 p^{4} - 5) (p + 6) = 8 p^{5} + 48 p^{4} - 5 p - 30\)

(Differentiëren)
\(f'(p) = 40 p^{4} + 192 p^{3} - 5 \text{.}\)

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

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

(Productregel)
\(f'(x) = -2 (-4 x^{2} - 5 x) + (-2 x + 7) (-8 x - 5) \text{.}\)

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

(Quotiëntregel)
\(f'(x) = {(-x - 7) ⋅ 4 - (4 x - 6) ⋅ -1 \over (-x - 7)^{2}} \text{.}\)

\(f'(x) = {(-4 x - 28) - (-4 x + 6) \over (-x - 7)^{2}} = {-34 \over (-x - 7)^{2}} \text{.}\)

(Quotiëntregel)
\(f'(p) = {(2 p + 8) ⋅ -14 p - -7 p^{2} ⋅ 2 \over (2 p + 8)^{2}} \text{.}\)

\(f'(p) = {(-28 p^{2} - 112 p) - -14 p^{2} \over (2 p + 8)^{2}} = {-14 p^{2} - 112 p \over (2 p + 8)^{2}} \text{.}\)