\(f'(x)=8⋅2⋅x^1+3\text{.}\)

\(f'(x)=16x+3\text{.}\)

\(f'(p)=-4⋅8⋅p^7-6⋅6⋅p^5-1⋅2⋅p^1\text{.}\)

\(f'(p)=-32p^7-36p^5-2p\text{.}\)

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

\(f'(a)=56a^7+\frac{4}{9}a+\frac{4}{5}\text{.}\)

(Haakjes wegwerken)
\(f(x)=(9x^3-2)(x+8)=9x^4+72x^3-2x-16\)

(Differentiëren)
\(f'(x)=36x^3+216x^2-2\text{.}\)

(Haakjes wegwerken)
\(f(a)=(5a^2+4)^2=25a^4+40a^2+16\)

(Differentiëren)
\(f'(a)=100a^3+80a\text{.}\)

(Herleiden)
\(f(p)={9 \over 4p^2}=\frac{9}{4}p^{-2}\)

(Differentiëren)
\(f'(p)=\frac{9}{4}⋅-2⋅p^{-3}=-\frac{9}{2}⋅p^{-3}\)

(Herleiden)
\(f'(p)=-\frac{9}{2}⋅{1 \over p^3}=-{9 \over 2p^3}\)

(Uitdelen)
\(f(a)={a^6 \over 2a^4}-{5a^2 \over 2a^4}=\frac{1}{2}a^2-\frac{5}{2}a^{-2}\)

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

(Herleiden)
\(f'(a)=a+{5 \over a^3}\)

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

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

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

(Kettingregel)
\(f'(x)=8⋅6⋅(9x-3)^5⋅9\)

(Herleiden)
\(f'(x)=432(9x-3)^5\text{.}\)

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

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

(Herleiden)
\(f'(x)=-10⋅(5x-3)^{-3}=-{10 \over (5x-3)^3}\)

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

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

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

(Herleiden)
\(f(a)=-{8 \over 3\sqrt{5a-4}}=-\frac{8}{3}⋅(5a-4)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(a)=-\frac{8}{3}⋅-\frac{1}{2}⋅(5a-4)^{-1\frac{1}{2}}⋅5\)

(Herleiden)
\(f'(a)=\frac{20}{3}⋅(5a-4)^{-1\frac{1}{2}}={20 \over 3(5a-4)\sqrt{5a-4}}\)