JEE Advanced 2014 · Paper 1 · Mathematics Q56

MathematicsInteger+3Question 56 of 60

The slope of the tangent to the curve $(y-x^5)^2=x(1+x^2)^2$ at the point $(1,3)$ is

Your answer

Answer and worked solution

Official answer: 8

Differentiate implicitly.
$2(y-x^5)(y'-5x^4)=(1+x^2)^2+4x^2(1+x^2).$

At $(1,3)$ . $y-x^5=2$ , and the right side is $4+8=12$ :
$4(y'-5)=12\implies y'=8.$

Answer: 8

JEE Advanced 2014 · Paper 1, Mathematics question 56