\(f'(a)=8⋅2⋅a^1+9\text{.}\)

\(f'(a)=16a+9\text{.}\)

\(f'(x)=-2⋅2⋅x^1-8\text{.}\)

\(f'(x)=-4x-8\text{.}\)

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

\(f'(a)=31\frac{1}{2}a^8+3\frac{3}{5}a^5+45a^4+1\frac{1}{2}\text{.}\)

(Haakjes wegwerken)
\(f(p)=(8p^4-6)(p-7)=8p^5-56p^4-6p+42\)

(Differentiëren)
\(f'(p)=40p^4-224p^3-6\text{.}\)

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

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

(Herleiden)
\(f(x)={8 \over 9x^2}=\frac{8}{9}x^{-2}\)

(Differentiëren)
\(f'(x)=\frac{8}{9}⋅-2⋅x^{-3}=-\frac{16}{9}⋅x^{-3}\)

(Herleiden)
\(f'(x)=-\frac{16}{9}⋅{1 \over x^3}=-{16 \over 9x^3}\)

(Herleiden)
\(f(p)=6p^2⋅\sqrt[7]{p^4}=6⋅p^2⋅p^{\frac{4}{7}}=6⋅p^{2\frac{4}{7}}\)

(Differentiëren)
\(f'(p)=6⋅2\frac{4}{7}⋅p^{1\frac{4}{7}}\)

(Herleiden)
\(f'(p)=15\frac{3}{7}⋅p^1⋅p^{\frac{4}{7}}=15\frac{3}{7}p⋅\sqrt[7]{p^4}\)

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

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

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

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

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

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

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

(Herleiden)
\(f(x)={3 \over 2\sqrt{x}}-9\sqrt{x}=\frac{3}{2}x^{-\frac{1}{2}}-9x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x)=\frac{3}{2}⋅-\frac{1}{2}⋅x^{-1\frac{1}{2}}-9⋅\frac{1}{2}⋅x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x)=-{3 \over 4x\sqrt{x}}-{9 \over 2\sqrt{x}}\)

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

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

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

(Herleiden)
\(f'(a)=-{5 \over 2a⋅\sqrt{a}}+{6 \over a^2⋅\sqrt{a}}\)

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

(Herleiden)
\(f'(a)=270(9a-2)^5\text{.}\)

(Herleiden)
\(f(x)={4 \over (2x-3)^5}=4⋅(2x-3)^{-5}\)

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

(Herleiden)
\(f'(x)=-40⋅(2x-3)^{-6}=-{40 \over (2x-3)^6}\)

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

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

(Herleiden)
\(f'(x)=-\frac{15}{2}⋅(3x+4)^{-\frac{1}{2}}=-{15 \over 2\sqrt{3x+4}}\)

(Herleiden)
\(f(p)={9 \over 8\sqrt{2p+3}}=\frac{9}{8}⋅(2p+3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(p)=\frac{9}{8}⋅-\frac{1}{2}⋅(2p+3)^{-1\frac{1}{2}}⋅2\)

(Herleiden)
\(f'(p)=-\frac{9}{8}⋅(2p+3)^{-1\frac{1}{2}}=-{9 \over 8(2p+3)\sqrt{2p+3}}\)