214k views
3 votes
How can i differentiate this equation?

How can i differentiate this equation?-example-1
User Rethab
by
8.3k points

1 Answer

4 votes


\bf y=\cfrac{2x^2-10x}{√(x)}\implies y=\cfrac{2x^2-10x}{x^{(1)/(2)}} \\\\\\ \cfrac{dy}{dx}=\stackrel{\textit{quotient rule}}{\cfrac{(4x-10)(√(x))~~-~~(2x^2-10x)\left( (1)/(2)x^{-(1)/(2)} \right)}{\left( x^{(1)/(2)} \right)^2}} \\\\\\ \cfrac{dy}{dx}=\cfrac{(4x-10)(√(x))~~-~~(2x^2-10x)\left( (1)/(2√(x)) \right)}{\left( x^{(1)/(2)} \right)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{(4x-10)(√(x))~~-~~\left( (2x^2-10x)/(2√(x)) \right)}{x}



\bf\cfrac{dy}{dx}=\cfrac{(4x-10)(√(x))~~-~~\left( (2x^2-10x)/(2√(x)) \right)}{x} \\\\\\ \cfrac{dy}{dx}=\cfrac{ ((4x-10)(√(x))(2√(x))~~-~~(2x^2-10x))/(2√(x))}{x} \\\\\\ \cfrac{dy}{dx}=\cfrac{(4x-10)(√(x))(2√(x))~~-~~(2x^2-10x)}{2x√(x)}



\bf \cfrac{dy}{dx}=\cfrac{(4x-10)2x~~-~~(2x^2-10x)}{2x√(x)}\implies \cfrac{dy}{dx}=\cfrac{8x^2-20x~~-~~(2x^2-10x)}{2x√(x)} \\\\\\ \cfrac{dy}{dx}=\cfrac{8x^2-20x~~-~~2x^2+10x}{2x√(x)} \implies \cfrac{dy}{dx}=\cfrac{6x^2-10x}{2x√(x)} \\\\\\ \cfrac{dy}{dx}=\cfrac{2x(3x-5)}{2x√(x)}\implies \cfrac{dy}{dx}=\cfrac{3x-5}{√(x)}

User Latika
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories