\(f'(x)=2⋅x^1+7\text{.}\)

\(f'(x)=2x+7\text{.}\)

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

\(f'(x)=-9x^8+35x^4+10x\text{.}\)

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

\(f'(a)=3\frac{3}{8}a^8+40a^7+1\frac{3}{7}a^4\text{.}\)

(Haakjes wegwerken)
\(f(p)=(9p^3+5)(p+6)=9p^4+54p^3+5p+30\)

(Differentiëren)
\(f'(p)=36p^3+162p^2+5\text{.}\)

(Haakjes wegwerken)
\(f(a)=(4a^2-1)^2=16a^4-8a^2+1\)

(Differentiëren)
\(f'(a)=64a^3-16a\text{.}\)

(Herleiden)
\(f(a)=-{5 \over 3a^9}=-\frac{5}{3}a^{-9}\)

(Differentiëren)
\(f'(a)=-\frac{5}{3}⋅-9⋅a^{-10}=15⋅a^{-10}\)

(Herleiden)
\(f'(a)=15⋅{1 \over a^{10}}={15 \over a^{10}}\)

(Kettingregel)
\(f'(a)=6⋅3⋅(\frac{7}{9}a+1)^2⋅\frac{7}{9}\)

(Herleiden)
\(f'(a)=14(\frac{7}{9}a+1)^2\text{.}\)

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

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

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

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

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

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

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

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

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

(Herleiden)
\(f(p)=8p⋅\sqrt[9]{p^8}=8⋅p^1⋅p^{\frac{8}{9}}=8⋅p^{1\frac{8}{9}}\)

(Differentiëren)
\(f'(p)=8⋅1\frac{8}{9}⋅p^{\frac{8}{9}}\)

(Herleiden)
\(f'(p)=15\frac{1}{9}⋅p^0⋅p^{\frac{8}{9}}=15\frac{1}{9}⋅\sqrt[9]{p^8}\)

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

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

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

(Kettingregel)
\(f'(x)=5⋅6⋅(4x^4+2x^3+3x^2)^5⋅(16x^3+6x^2+6x)\)

(Herleiden)
\(f'(x)=(480x^3+180x^2+180x)⋅(4x^4+2x^3+3x^2)^5\)

\(f(x)=5⋅6^{-3x-1}⋅\ln(6)⋅-3=-15⋅6^{-3x-1}⋅\ln(6)\)

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

\(f'(x)={(-54x+45)-(-54x+48) \over (6x-5)^2}={-3 \over (6x-5)^2}\text{.}\)

(Quotiëntregel)
\(f'(a)={(-2a-1)⋅-8a--4a^2⋅-2 \over (-2a-1)^2}\text{.}\)

\(f'(a)={(16a^2+8a)-8a^2 \over (-2a-1)^2}={8a^2+8a \over (-2a-1)^2}\text{.}\)