Question

Let f(x) = (-6x^6\sqrt(x))+(8)(x^(3)\sqrt(x)). Find f'(x).

Answer 1

`f(x) =-6x^6√(x)+8x^3 √(x)\\\\f'(x) =\bigg(-6x^6√(x)+8x^3 √(x)\bigg)'=\bigg(-6x^6\cdot x^{ (1)/(2) }\bigg)'+\bigg(8x^3\cdot x^{ (1)/(2) }\bigg)'=\\\\=-6\cdot \bigg(x^{6 (1)/(2) }\bigg)'+8\cdot \bigg(x^{3 (1)/(2) }\bigg)'=-6\cdot 6 (1)/(2)\cdot x^{5 (1)/(2) }+8\cdot 3 (1)/(2) \cdot x^{2 (1)/(2) }=\\\\=-39x^5 √(x) +28x^2 √(x)`