\(f'(x)=3⋅2⋅x^1+2\text{.}\)

\(f'(x)=6x+2\text{.}\)

\(f'(a)=-5⋅9⋅a^8-6⋅3⋅a^2+8\text{.}\)

\(f'(a)=-45a^8-18a^2+8\text{.}\)

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

\(f'(a)=9\frac{1}{3}a^6+4\frac{2}{7}a^5+15a^4\text{.}\)

(Haakjes wegwerken)
\(f(x)=(8x^3-7)(x-1)=8x^4-8x^3-7x+7\)

(Differentiëren)
\(f'(x)=32x^3-24x^2-7\text{.}\)

(Haakjes wegwerken)
\(f(p)=(3p^5-4)^2=9p^{10}-24p^5+16\)

(Differentiëren)
\(f'(p)=90p^9-120p^4\text{.}\)

(Herleiden)
\(f(p)={4 \over 3p^6}=\frac{4}{3}p^{-6}\)

(Differentiëren)
\(f'(p)=\frac{4}{3}⋅-6⋅p^{-7}=-8⋅p^{-7}\)

(Herleiden)
\(f'(p)=-8⋅{1 \over p^7}=-{8 \over p^7}\)

(Herleiden)
\(f(x)=-9x^2⋅\sqrt[8]{x^3}=-9⋅x^2⋅x^{\frac{3}{8}}=-9⋅x^{2\frac{3}{8}}\)

(Differentiëren)
\(f'(x)=-9⋅2\frac{3}{8}⋅x^{1\frac{3}{8}}\)

(Herleiden)
\(f'(x)=-21\frac{3}{8}⋅x^1⋅x^{\frac{3}{8}}=-21\frac{3}{8}x⋅\sqrt[8]{x^3}\)

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

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

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

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

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

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

(Herleiden)
\(f'(x)=11\frac{1}{5}x⋅\sqrt[5]{x^4}-{1 \over 5x⋅\sqrt[5]{x}}\)

(Herleiden)
\(f(a)={9 \over 4\sqrt{a}}-6\sqrt{a}=\frac{9}{4}a^{-\frac{1}{2}}-6a^{\frac{1}{2}}\)

(Differentiëren)
\(f'(a)=\frac{9}{4}⋅-\frac{1}{2}⋅a^{-1\frac{1}{2}}-6⋅\frac{1}{2}⋅a^{-\frac{1}{2}}\)

(Herleiden)
\(f'(a)=-{9 \over 8a\sqrt{a}}-{3 \over \sqrt{a}}\)

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

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

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

(Herleiden)
\(f'(x)={3 \over 2x^2⋅\sqrt{x}}+{25 \over 2x^3⋅\sqrt{x}}\)

(Kettingregel)
\(f'(x)=9⋅7⋅(2x+3)^6⋅2\)

(Herleiden)
\(f'(x)=126(2x+3)^6\text{.}\)

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

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

(Herleiden)
\(f'(a)=8⋅(2a+3)^{-5}={8 \over (2a+3)^5}\)

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

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

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

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

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

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