\(f'(p)=9⋅3⋅p^2+5\text{.}\)

\(f'(p)=27p^2+5\text{.}\)

\(f'(a)=7⋅9⋅a^8+4⋅8⋅a^7\text{.}\)

\(f'(a)=63a^8+32a^7\text{.}\)

\(f'(a)=3⋅9⋅a^8+\frac{4}{9}⋅7⋅a^6+\frac{3}{5}⋅3⋅a^2\text{.}\)

\(f'(a)=27a^8+3\frac{1}{9}a^6+1\frac{4}{5}a^2\text{.}\)

(Haakjes wegwerken)
\(f(x)=(7x^4+9)(x-6)=7x^5-42x^4+9x-54\)

(Differentiëren)
\(f'(x)=35x^4-168x^3+9\text{.}\)

(Haakjes wegwerken)
\(f(x)=(4x^3-2)^2=16x^6-16x^3+4\)

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

(Herleiden)
\(f(a)={5 \over 8a^5}=\frac{5}{8}a^{-5}\)

(Differentiëren)
\(f'(a)=\frac{5}{8}⋅-5⋅a^{-6}=-\frac{25}{8}⋅a^{-6}\)

(Herleiden)
\(f'(a)=-\frac{25}{8}⋅{1 \over a^6}=-{25 \over 8a^6}\)

(Uitdelen)
\(f(x)={x^6 \over 5x^4}+{3x \over 5x^4}=\frac{1}{5}x^2+\frac{3}{5}x^{-3}\)

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

(Herleiden)
\(f'(x)=\frac{2}{5}x-{9 \over 5x^4}\)

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

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

(Herleiden)
\(f'(a)=-{7 \over 12a\sqrt{a}}+{1 \over \sqrt{a}}\)

(Kettingregel)
\(f'(x)=9⋅6⋅(3x-2)^5⋅3\)

(Herleiden)
\(f'(x)=162(3x-2)^5\text{.}\)

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

(Kettingregel)
\(f'(a)=1⋅-5⋅(3a-4)^{-6}⋅3\)

(Herleiden)
\(f'(a)=-15⋅(3a-4)^{-6}=-{15 \over (3a-4)^6}\)

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

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

(Herleiden)
\(f'(a)=-\frac{9}{10}⋅(3a+1)^{-\frac{1}{2}}=-{9 \over 10\sqrt{3a+1}}\)

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

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

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