\(f'(x)=9⋅2⋅x^1+2\text{.}\)

\(f'(x)=18x+2\text{.}\)

\(f'(a)=-9⋅9⋅a^8+4⋅6⋅a^5-1\text{.}\)

\(f'(a)=-81a^8+24a^5-1\text{.}\)

\(f'(a)=1\frac{2}{7}⋅9⋅a^8+1\frac{1}{2}⋅7⋅a^6+1\frac{1}{2}⋅5⋅a^4+\frac{1}{5}⋅4⋅a^3\text{.}\)

\(f'(a)=11\frac{4}{7}a^8+10\frac{1}{2}a^6+7\frac{1}{2}a^4+\frac{4}{5}a^3\text{.}\)

Haakjes wegwerken geeft \(f(x)=(8x^3+4)(x-5)=8x^4-40x^3+4x-20\)

Differentiëren geeft \(f'(x)=32x^3-120x^2+4\text{.}\)

Haakjes wegwerken geeft \(f(p)=(5p^2+3)^2=25p^4+30p^2+9\)

Differentiëren geeft \(f'(p)=100p^3+60p\text{.}\)

De productregel geeft \(f'(x)=-5(4x^2+6x)+(-5x+3)(8x+6)\text{.}\)

De productregel geeft \(f'(x)=(8x+1)(-7x^2+6x-5)+(4x^2+x)(-14x+6)\text{.}\)

De quotiëntregel geeft
\(f'(a)={(-5a-4)⋅3-(3a-6)⋅-5 \over (-5a-4)^2}\text{.}\)

\(f'(a)={(-15a-12)-(-15a+30) \over (-5a-4)^2}={-42 \over (-5a-4)^2}\text{.}\)

De quotiëntregel geeft
\(f'(p)={(-8p-1)⋅-14p--7p^2⋅-8 \over (-8p-1)^2}\text{.}\)

\(f'(p)={(112p^2+14p)-56p^2 \over (-8p-1)^2}={56p^2+14p \over (-8p-1)^2}\text{.}\)