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Question:

The slope of the tangent to the curve (y-x5)2 = x(1+x2)2 at the point (1,3) is?

Solution:

2(y-x5)(dy/dx - 5x4) = (1+x2)2 + x(2(1+x2)(2x))
Now put x=1, y=3 and dy/dx = m
2(3-1)(m-5) = (1+1)2 + (1)(2(1+1)(2))
m-5 = 4 + 8
2(2)(m-5) = 12
4(m-5) = 12
m - 5 = 3
m = 8
dy/dx = m = 8