\(f'(x)=2⋅2⋅x^1+5\text{.}\)

\(f'(x)=4x+5\text{.}\)

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

\(f'(a)=27a^8+35a^4+32a^3+12a^2\text{.}\)

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

\(f'(a)=2a^7+20a^4+1\frac{1}{3}a\text{.}\)

(Haakjes wegwerken)
\(f(p)=(7p^5+4)(p-9)=7p^6-63p^5+4p-36\)

(Differentiëren)
\(f'(p)=42p^5-315p^4+4\text{.}\)

(Haakjes wegwerken)
\(f(x)=(3x^2+4)^2=9x^4+24x^2+16\)

(Differentiëren)
\(f'(x)=36x^3+48x\text{.}\)

(Herleiden)
\(f(x)=-{4 \over 5x^7}=-\frac{4}{5}x^{-7}\)

(Differentiëren)
\(f'(x)=-\frac{4}{5}⋅-7⋅x^{-8}=\frac{28}{5}⋅x^{-8}\)

(Herleiden)
\(f'(x)=\frac{28}{5}⋅{1 \over x^8}={28 \over 5x^8}\)

(Kettingregel)
\(f'(p)=8⋅3⋅(5p-7)^2⋅5\)

(Herleiden)
\(f'(p)=120(5p-7)^2\text{.}\)

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

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

(Herleiden)
\(f'(a)=-24⋅(2a+5)^{-5}=-{24 \over (2a+5)^5}\)

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

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

(Herleiden)
\(f'(a)=-\frac{9}{10}⋅(3a+2)^{-\frac{1}{2}}=-{9 \over 10\sqrt{3a+2}}\)

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

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

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

(Herleiden)
\(f(a)=9a⋅\sqrt[9]{a^7}=9⋅a^1⋅a^{\frac{7}{9}}=9⋅a^{1\frac{7}{9}}\)

(Differentiëren)
\(f'(a)=9⋅1\frac{7}{9}⋅a^{\frac{7}{9}}\)

(Herleiden)
\(f'(a)=16⋅a^0⋅a^{\frac{7}{9}}=16⋅\sqrt[9]{a^7}\)

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

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

(Herleiden)
\(f'(x)=-{3 \over 16x\sqrt{x}}-{4 \over \sqrt{x}}\)

(Kettingregel)
\(f'(a)=6⋅4⋅(5a^4+2a^3+3)^3⋅(20a^3+6a^2)\)

(Herleiden)
\(f'(a)=(480a^3+144a^2)⋅(5a^4+2a^3+3)^3\)

\(f(x)=3⋅4^{-2x^3-x}⋅\ln(4)⋅(-6x^2-1)=(-18x^2-3)⋅4^{-2x^3-x}⋅\ln(4)\)

(Quotiëntregel)
\(f'(a)={(5a+1)⋅4-(4a-7)⋅5 \over (5a+1)^2}\text{.}\)

\(f'(a)={(20a+4)-(20a-35) \over (5a+1)^2}={39 \over (5a+1)^2}\text{.}\)

(Quotiëntregel)
\(f'(p)={(5p-5)⋅16p-8p^2⋅5 \over (5p-5)^2}\text{.}\)

\(f'(p)={(80p^2-80p)-40p^2 \over (5p-5)^2}={40p^2-80p \over (5p-5)^2}\text{.}\)