Question

F(x) = 4√(2x³-1)
F'(x) =.....?

Answer 1

`\large\boxed{f'(x)=(12x^2)/(√(2x^3-1))}`

Explanation:

`f(x)=4√(2x^3-1)=4\left(2x^3-1\right)^(1)/(2)\\\\f'(x)=4\cdot(1)/(2)(2x^3-1)^{-(1)/(2)}\cdot3\cdot2x^2=(12x^2)/((2x^3-1)^(1)/(2))=(12x^2)/(√(2x^3-1))\\\\\text{used}\\\\√(a)=a^(1)/(2)\\\\\bigg[f\left(g(x)\right)\bigg]'=f'(g(x))\cdot g'(x)\\\\\bigg[nf(x)\bigg]'=nf'(x)\\\\(x^n)'=nx^(n-1)`