Question

`F(x)=(6 √(x) -2)(5 √(x) +7)`

Answer 1

`\bf f(x)=(6√(x)-2)(5√(x)+7) \\\\\\ \cfrac{dy}{dx}=\stackrel{product~rule}{\left( 6\cdot (1)/(2)x^{-(1)/(2)} \right)(5x^{(1)/(2)}+7)~~+~~(6x^{(1)/(2)}-2)\left(5\cdot (1)/(2)x^{-(1)/(2)} \right)} \\\\\\ \cfrac{dy}{dx}=\left(\cfrac{6}{2}\cdot \cfrac{1}{√(x)} \right)(5x^{(1)/(2)}+7)~~+~~2(3x^{(1)/(2)}-1)\left(\cfrac{5}{2}x^{-(1)/(2)} \right)`


`\bf \cfrac{dy}{dx}=\left(3\cdot \cfrac{1}{√(x)} \right)(5x^{(1)/(2)}+7)~~+~~2\cdot \cfrac{5}{2}(3x^{(1)/(2)}-1)\left(\cfrac{1}{√(x)} \right) \\\\\\ \cfrac{dy}{dx}=\cfrac{3(5√(x)+7)}{√(x)}~~+~~\cfrac{5(3√(x)-1)}{√(x)}\\\\\\ \cfrac{dy}{dx}=\cfrac{15√(x)+21~~+~~15√(x)-5}{√(x)} \\\\\\ \cfrac{dy}{dx}=\cfrac{30√(x)+16}{√(x)}`