\(f'(x)=2⋅2⋅x^1+6\text{.}\)

\(f'(x)=4x+6\text{.}\)

\(f'(a)=-1⋅9⋅a^8-2⋅5⋅a^4-7⋅3⋅a^2\text{.}\)

\(f'(a)=-9a^8-10a^4-21a^2\text{.}\)

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

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

(Haakjes wegwerken)
\(f(x)=(9x^3-4)(x-2)=9x^4-18x^3-4x+8\)

(Differentiëren)
\(f'(x)=36x^3-54x^2-4\text{.}\)

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

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

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

(Productregel)
\(f'(p)=(14p-2)(-4p^2-7p+8)+(7p^2-2p)(-8p-7)\text{.}\)

(Quotiëntregel)
\(f'(a)={(5a-2)⋅1-(a-6)⋅5 \over (5a-2)^2}\text{.}\)

\(f'(a)={(5a-2)-(5a-30) \over (5a-2)^2}={28 \over (5a-2)^2}\text{.}\)

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

\(f'(x)={(-4x^2+12x)--2x^2 \over (2x-6)^2}={-2x^2+12x \over (2x-6)^2}\text{.}\)

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

(Differentiëren)
\(f'(a)=-\frac{5}{3}⋅-6⋅a^{-7}=10⋅a^{-7}\)

(Herleiden)
\(f'(a)=10⋅{1 \over a^7}={10 \over a^7}\)

(Herleiden)
\(f(a)=-7a⋅\sqrt[5]{a^4}=-7⋅a^1⋅a^{\frac{4}{5}}=-7⋅a^{1\frac{4}{5}}\)

(Differentiëren)
\(f'(a)=-7⋅1\frac{4}{5}⋅a^{\frac{4}{5}}\)

(Herleiden)
\(f'(a)=-12\frac{3}{5}⋅a^0⋅a^{\frac{4}{5}}=-12\frac{3}{5}⋅\sqrt[5]{a^4}\)

(Uitdelen)
\(f(p)={p^8 \over 4p^5}+{5p^2 \over 4p^5}=\frac{1}{4}p^3+\frac{5}{4}p^{-3}\)

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

(Herleiden)
\(f'(p)=\frac{3}{4}p^2-{15 \over 4p^4}\)

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

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

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

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

(Herleiden)
\(f(x)={7 \over 5\sqrt{x}}+3\sqrt{x}=\frac{7}{5}x^{-\frac{1}{2}}+3x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x)=\frac{7}{5}⋅-\frac{1}{2}⋅x^{-1\frac{1}{2}}+3⋅\frac{1}{2}⋅x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x)=-{7 \over 10x\sqrt{x}}+{3 \over 2\sqrt{x}}\)

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

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

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

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

(Kettingregel)
\(f'(p)=6⋅3⋅(\frac{3}{4}p-8)^2⋅\frac{3}{4}\)

(Herleiden)
\(f'(p)=13\frac{1}{2}(\frac{3}{4}p-8)^2\text{.}\)

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

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

(Herleiden)
\(f'(x)=60⋅(5x-1)^{-5}={60 \over (5x-1)^5}\)

(Herleiden)
\(f(x)=-\frac{5}{8}\sqrt{3x-5}=-\frac{5}{8}⋅(3x-5)^{\frac{1}{2}}\text{.}\)

(Kettingregel)
\(f'(x)=-\frac{5}{8}⋅\frac{1}{2}⋅(3x-5)^{-\frac{1}{2}}⋅3\)

(Herleiden)
\(f'(x)=-\frac{15}{16}⋅(3x-5)^{-\frac{1}{2}}=-{15 \over 16\sqrt{3x-5}}\)

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

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

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

(Kettingregel)
\(f'(a)=6⋅3⋅(2a^4+a^3+4)^2⋅(8a^3+3a^2)\)

(Herleiden)
\(f'(a)=(144a^3+54a^2)⋅(2a^4+a^3+4)^2\)

\(f(a)=9a^2⋅e^{2a-1}+(3a^3+2)⋅e^{2a-1}⋅2\)
\(\text{ }=9a^2⋅e^{2a-1}+(6a^3+4)⋅e^{2a-1}\)
\(\text{ }=(6a^3+9a^2+4)⋅e^{2a-1}\)

\(f(p)=-5⋅e^{-4p^2+3p}⋅(-8p+3)=(40p-15)⋅e^{-4p^2+3p}\)