Differentiëren

\(f'(a)=7⋅3⋅a^2+8\text{.}\)

\(f'(a)=21a^2+8\text{.}\)

\(f'(x)=-1⋅9⋅x^8+6⋅7⋅x^6+5⋅2⋅x^1\text{.}\)

\(f'(x)=-9x^8+42x^6+10x\text{.}\)

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

\(f'(p)=56p^7+14p^6+2\frac{2}{9}p^3\text{.}\)

(Haakjes wegwerken)
\(f(x)=(3x^2-4)(x-9)=3x^3-27x^2-4x+36\)

(Differentiëren)
\(f'(x)=9x^2-54x-4\text{.}\)

(Haakjes wegwerken)
\(f(a)=(5a^4+1)^2=25a^8+10a^4+1\)

(Differentiëren)
\(f'(a)=200a^7+40a^3\text{.}\)

(Herleiden)
\(f(x)=2x^3⋅\sqrt[8]{x^7}=2⋅x^3⋅x^{\frac{7}{8}}=2⋅x^{3\frac{7}{8}}\)

(Differentiëren)
\(f'(x)=2⋅3\frac{7}{8}⋅x^{2\frac{7}{8}}\)

(Herleiden)
\(f'(x)=7\frac{3}{4}⋅x^2⋅x^{\frac{7}{8}}=7\frac{3}{4}x^2⋅\sqrt[8]{x^7}\)

(Herleiden)
\(f(p)={9 \over 4p^9}=\frac{9}{4}p^{-9}\)

(Differentiëren)
\(f'(p)=\frac{9}{4}⋅-9⋅p^{-10}=-\frac{81}{4}⋅p^{-10}\)

(Herleiden)
\(f'(p)=-\frac{81}{4}⋅{1 \over p^{10}}=-{81 \over 4p^{10}}\)

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

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

(Herleiden)
\(f'(a)=-{3 \over 14a\sqrt{a}}+{7 \over 2\sqrt{a}}\)

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

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

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

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

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

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

(Herleiden)
\(f'(a)=6\frac{2}{3}⋅\sqrt[3]{a^2}-{5 \over 3a⋅\sqrt[3]{a}}\)

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

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

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

(Herleiden)
\(f'(p)=-{5 \over 2p⋅\sqrt{p}}+{9 \over 2p^2⋅\sqrt{p}}\)

(Quotiëntregel)
\(f'(a)={(-6a-5)⋅5-(5a+8)⋅-6 \over (-6a-5)^2}\text{.}\)

\(f'(a)={(-30a-25)-(-30a-48) \over (-6a-5)^2}={23 \over (-6a-5)^2}\text{.}\)

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

\(f'(x)={(4x^2+16x)-2x^2 \over (2x+8)^2}={2x^2+16x \over (2x+8)^2}\text{.}\)

(Kettingregel)
\(f'(a)=8⋅4⋅(\frac{4}{7}a+2)^3⋅\frac{4}{7}\)

(Herleiden)
\(f'(a)=18\frac{2}{7}(\frac{4}{7}a+2)^3\text{.}\)

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

(Herleiden)
\(f'(p)=(192p^3+72p^2+72)⋅(2p^4+p^3+3p)^5\)

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

(Kettingregel)
\(f'(x)=1⋅-5⋅(2x+4)^{-6}⋅2\)

(Herleiden)
\(f'(x)=-10⋅(2x+4)^{-6}=-{10 \over (2x+4)^6}\)

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

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

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

(Herleiden)
\(f(a)=-{2 \over 9\sqrt{3a+4}}=-\frac{2}{9}⋅(3a+4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a)=-\frac{2}{9}⋅-\frac{1}{2}⋅(3a+4)^{-1\frac{1}{2}}⋅3\)

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

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

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

(Productregel)
\(f'(x)=-8(-6x^2-3x)+(-8x-2)(-12x-3)\text{.}\)

(Productregel)
\(f'(a)=(-14a-1)(-9a^2+7a-4)+(-7a^2-a)(-18a+7)\text{.}\)