Q36 / 60 · JEE Advanced 2014 (Paper 1) · Mathematics

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

Correct answer: 8

Solution

2 (y - x^{5}) (\frac{d y}{d x} - 5 x^{4})

= 1 {(1 + x^{2})}^{2} + (x) (2 (1 + x^{2}) (2 x))

Now put

x = 1, y = 3

and

\frac{d y}{d x} = m .

2 (3 - 1) (m - 5) = 1 (4) + (1) (4) (2)

m - 5 = \frac{12}{4}

m = 5 + 3 = 8

\frac{d y}{d x} = m = 8 .

Hence, the correct answer is 8.

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