Application of Derivatives 1 Question 22

####22. The slope of the tangent to the curve (y−x5)2=x(1+x2)2 at the point (1,3) is

(2014 Adv.)

Show Answer

Answer:

(8)

Solution:

  1. Slope of tangent at the point (x1,y1) is $\frac{d y}{d x}{ }{\left(x{1}, y_{1}\right)}$.

Given curve, (y−x5)2=x(1+x2)2

⇒2(y−x5)dydx−5x4=(1+x2)2+2x(1+x2)⋅2x

Put x=1 and y=3,dy/dx=8

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