\(f'(a)=6⋅2⋅a^1+2\text{.}\)

\(f'(a)=12a+2\text{.}\)

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

\(f'(a)=45a^4+3a^2+6a\text{.}\)

\(f'(x)=1\frac{1}{6}⋅8⋅x^7+\frac{1}{3}⋅6⋅x^5+\frac{1}{8}⋅5⋅x^4+\frac{1}{2}\text{.}\)

\(f'(x)=9\frac{1}{3}x^7+2x^5+\frac{5}{8}x^4+\frac{1}{2}\text{.}\)

(Haakjes wegwerken)
\(f(p)=(9p^2-3)(p-6)=9p^3-54p^2-3p+18\)

(Differentiëren)
\(f'(p)=27p^2-108p-3\text{.}\)

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

(Differentiëren)
\(f'(x)=24x^5+48x^2\text{.}\)

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

(Productregel)
\(f'(x)=(-14x-1)(2x^2+9x+3)+(-7x^2-x)(4x+9)\text{.}\)

(Quotiëntregel)
\(f'(p)={(-7p-1)⋅9-(9p+1)⋅-7 \over (-7p-1)^2}\text{.}\)

\(f'(p)={(-63p-9)-(-63p-7) \over (-7p-1)^2}={-2 \over (-7p-1)^2}\text{.}\)

(Quotiëntregel)
\(f'(x)={(-5x+2)⋅-18x--9x^2⋅-5 \over (-5x+2)^2}\text{.}\)

\(f'(x)={(90x^2-36x)-45x^2 \over (-5x+2)^2}={45x^2-36x \over (-5x+2)^2}\text{.}\)

(Herleiden)
\(f(p)=-{6 \over 7p^8}=-\frac{6}{7}p^{-8}\)

(Differentiëren)
\(f'(p)=-\frac{6}{7}⋅-8⋅p^{-9}=\frac{48}{7}⋅p^{-9}\)

(Herleiden)
\(f'(p)=\frac{48}{7}⋅{1 \over p^9}={48 \over 7p^9}\)

(Herleiden)
\(f(x)=-5x^2⋅\sqrt[9]{x^4}=-5⋅x^2⋅x^{\frac{4}{9}}=-5⋅x^{2\frac{4}{9}}\)

(Differentiëren)
\(f'(x)=-5⋅2\frac{4}{9}⋅x^{1\frac{4}{9}}\)

(Herleiden)
\(f'(x)=-12\frac{2}{9}⋅x^1⋅x^{\frac{4}{9}}=-12\frac{2}{9}x⋅\sqrt[9]{x^4}\)

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

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

(Herleiden)
\(f'(a)=a+{5 \over a^3}\)

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

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

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

(Herleiden)
\(f'(a)=6\frac{2}{3}⋅\sqrt[3]{a^2}+{1 \over 3a⋅\sqrt[3]{a}}\)

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

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

(Herleiden)
\(f'(x)=-{7 \over 8x\sqrt{x}}-{7 \over 2\sqrt{x}}\)

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

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

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

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

(Kettingregel)
\(f'(a)=6⋅4⋅(7a+5)^3⋅7\)

(Herleiden)
\(f'(a)=168(7a+5)^3\text{.}\)

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

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

(Herleiden)
\(f'(a)=60⋅(3a+2)^{-6}={60 \over (3a+2)^6}\)

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

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

(Herleiden)
\(f'(p)=-\frac{15}{2}⋅(5p-1)^{-\frac{1}{2}}=-{15 \over 2\sqrt{5p-1}}\)

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

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

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

(Kettingregel)
\(f'(x)=2⋅5⋅(6x^4+4x^2+1)^4⋅(24x^3+8x)\)

(Herleiden)
\(f'(x)=(240x^3+80x)⋅(6x^4+4x^2+1)^4\)

\(f(x)=-15x^2⋅e^{-5x-4}+(-5x^3-2)⋅e^{-5x-4}⋅-5\)
\(\text{ }=-15x^2⋅e^{-5x-4}+(25x^3+10)⋅e^{-5x-4}\)
\(\text{ }=(25x^3-15x^2+10)⋅e^{-5x-4}\)

\(f(p)=6⋅3^{-2p^2+5p}⋅\ln(3)⋅(-4p+5)=(-24p+30)⋅3^{-2p^2+5p}⋅\ln(3)\)