\(f'(x)=2⋅x^1+6\text{.}\)

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

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

\(f'(a)=-63a^6+15a^4+15a^2-3\text{.}\)

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

\(f'(p)=2p^7+6\frac{6}{7}p^5+9p^2+6p\text{.}\)

Haakjes wegwerken geeft \(f(a)=(7a^4+8)(a+9)=7a^5+63a^4+8a+72\)

Differentiëren geeft \(f'(a)=35a^4+252a^3+8\text{.}\)

Haakjes wegwerken geeft \(f(x)=(3x^2+1)^2=9x^4+6x^2+1\)

Differentiëren geeft \(f'(x)=36x^3+12x\text{.}\)

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

De productregel geeft \(f'(x)=(10x-1)(3x^2-5x+1)+(5x^2-x)(6x-5)\text{.}\)

De quotiëntregel geeft
\(f'(a)={(-4a-8)⋅-5-(-5a-1)⋅-4 \over (-4a-8)^2}\text{.}\)

\(f'(a)={(20a+40)-(20a+4) \over (-4a-8)^2}={36 \over (-4a-8)^2}\text{.}\)

De quotiëntregel geeft
\(f'(p)={(-2p-9)⋅-2p--p^2⋅-2 \over (-2p-9)^2}\text{.}\)

\(f'(p)={(4p^2+18p)-2p^2 \over (-2p-9)^2}={2p^2+18p \over (-2p-9)^2}\text{.}\)