\(f'(p)=4⋅3⋅p^2+7\text{.}\)

\(f'(p)=12p^2+7\text{.}\)

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

\(f'(a)=21a^6+36a^5-16a^3\text{.}\)

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

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

Haakjes wegwerken geeft \(f(x)=(6x^2+5)(x-8)=6x^3-48x^2+5x-40\)

Differentiëren geeft \(f'(x)=18x^2-96x+5\text{.}\)

Haakjes wegwerken geeft \(f(x)=(4x^2+1)^2=16x^4+8x^2+1\)

Differentiëren geeft \(f'(x)=64x^3+16x\text{.}\)

De productregel geeft \(f'(x)=1(-8x^2-4x)+(x-2)(-16x-4)\text{.}\)

De productregel geeft \(f'(p)=(-16p-4)(-9p^2+6p-6)+(-8p^2-4p)(-18p+6)\text{.}\)

De quotiëntregel geeft
\(f'(x)={(8x-2)⋅5-(5x-8)⋅8 \over (8x-2)^2}\text{.}\)

\(f'(x)={(40x-10)-(40x-64) \over (8x-2)^2}={54 \over (8x-2)^2}\text{.}\)

De quotiëntregel geeft
\(f'(a)={(-7a+9)⋅6a-3a^2⋅-7 \over (-7a+9)^2}\text{.}\)

\(f'(a)={(-42a^2+54a)--21a^2 \over (-7a+9)^2}={-21a^2+54a \over (-7a+9)^2}\text{.}\)