Jika f(x) = 6√2x^2+4x maka nilai

f(x) = 6√(2x^2 + 4x) = 6(2x^2 + 4x)^1/2

df(x)/dx = f'(x) = 3(2x^2 + 4x)^-1/2 . (4x + 4) = 3(4x + 4)/√(2x^2 + 4x)
df(2)/dx = f'(2) = 3(4.2 + 4)/√(2.2^2 + 4.2) = 3(12)/√16 = 36/4 = 9

[tex]\displaystyle f(x)=6\sqrt{2x^2+4x}\\f(x)=6(2x^2+4x)^\frac12\\\\\frac{d}{dx}f(x)=6\cdot\frac12\cdot(4x+4)(2x^2+4x)^{\frac12-1}\\\frac{d}{dx}f(x)=3(4x+4)(2x^2+4x)^{-\frac12}\\\\\frac{d}{dx}f(2)=3(4(2)+4)(2(2)^2+4(2))^{-\frac12}\\\frac{d}{dx}f(2)=3(8+4)(8+8)^{-\frac12}\\\frac{d}{dx}f(2)=3(12)(16)^{-\frac12}\\\frac{d}{dx}f(2)=3(12)\cdot\frac{1}{\sqrt{16}}\\\frac{d}{dx}f(2)=3(12)\cdot\frac{1}{4}\\\boxed{\boxed{\frac{d}{dx}f(2)=9}}[/tex]