[tex]f(x) =-6x^6\sqrt{x}+8x^3 \sqrt{x}\\\\f'(x) =\bigg(-6x^6\sqrt{x}+8x^3 \sqrt{x}\bigg)'=\bigg(-6x^6\cdot x^{ \frac{1}{2} }\bigg)'+\bigg(8x^3\cdot x^{ \frac{1}{2} }\bigg)'=\\\\=-6\cdot \bigg(x^{6 \frac{1}{2} }\bigg)'+8\cdot \bigg(x^{3 \frac{1}{2} }\bigg)'=-6\cdot 6 \frac{1}{2}\cdot x^{5 \frac{1}{2} }+8\cdot 3 \frac{1}{2} \cdot x^{2 \frac{1}{2} }=\\\\=-39x^5 \sqrt{x} +28x^2 \sqrt{x} [/tex]
