A curve has equation (x+y)^2=x*y^2, find the gradient of the curve at a point where x=1
- Differentiating left hand side: 2(x+y)(1+dy/dx) from the chain rule 2. Differentiating right hand side: y2+2xy(dy/dx) from the product rule 3. Equating sides and taking out factors of dy/dx to rearrange for dy/dx: dy/dx=[y2-2(x+y)]/[2(x+y)-2xy] 4. Substitute x=1 into original expression and solving for y (i.e. solving (1+y)2=y2) gives y=-1/2 5. Substituting x=1 and y=-1/2 into the expression for dy/dx gives dy/dx=-3/8
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