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Find dy/dx if y=a^2x + x/2x+1 |
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Answer» ain rule will be applied…Consider (2x+1) = aNow differentiate on both SIDES with respect to ‘a’, we get,2dx/da = 1So, dx/da = 1/2 …(Eqn. 1)Now, put (2x+1)=a in the main equation, you’ll gety= a^5Differentiating on both sides with respect to ‘a’ we get,dy/da= 5a^4 …(Eqn. 2)Now divide (Eqn. 2) by (Eqn. 1), we get(dy/da)/(dx/da) =5a^4/(1/2)So, dy/dx= 10a^4Resubstituting value of ‘a’, we getdy/dx= 10(2x+1)^4Method 2:This is also the CHAIN rule but with less steps:Consider (2x+1) is any variable and differentiate it the same WAY as you would differentiate y=x^nWhich is dy/dx = n*x^(n-1)So differentiation the main equation we get,dy/dx= 5*(2x+1)^4 * d(2x+1)/dx[The point to be noted here is after differentiating the bracket considering it as a variable, we need to again mulply with the DIFFERENTIAL of the bracket wrt x]So we get,dy/dx= 10*(2x+1)^4AND that’s your answer…Do remember the following Chain Rule:dy/dx= (dy/da)* (da/dx)Hope it helps…Feel good :) |
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