\(f'(p)=6⋅3⋅p^2+7\text{.}\)

\(f'(p)=18p^2+7\text{.}\)

\(f'(a)=7⋅8⋅a^7+2⋅3⋅a^2+8\text{.}\)

\(f'(a)=56a^7+6a^2+8\text{.}\)

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

\(f'(x)=6\frac{3}{4}x^8+16x^3+1\frac{5}{9}x\text{.}\)

(Haakjes wegwerken)
\(f(x)=(8x^2-7)(x-3)=8x^3-24x^2-7x+21\)

(Differentiëren)
\(f'(x)=24x^2-48x-7\text{.}\)

(Haakjes wegwerken)
\(f(a)=(4a^2-3)^2=16a^4-24a^2+9\)

(Differentiëren)
\(f'(a)=64a^3-48a\text{.}\)

(Productregel)
\(f'(x)=8(5x^2-6x)+(8x-2)(10x-6)\text{.}\)

(Productregel)
\(f'(a)=(14a-9)(-2a^2+8a+2)+(7a^2-9a)(-4a+8)\text{.}\)

(Quotiëntregel)
\(f'(p)={(-3p+2)⋅-1-(-p-9)⋅-3 \over (-3p+2)^2}\text{.}\)

\(f'(p)={(3p-2)-(3p+27) \over (-3p+2)^2}={-29 \over (-3p+2)^2}\text{.}\)

(Quotiëntregel)
\(f'(x)={(-2x+6)⋅-10x--5x^2⋅-2 \over (-2x+6)^2}\text{.}\)

\(f'(x)={(20x^2-60x)-10x^2 \over (-2x+6)^2}={10x^2-60x \over (-2x+6)^2}\text{.}\)