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JEE Previous Year Question

$m is the slope of a tangent to the curve e^{y} = 1 + x^{2} at x = 1 then m =$

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $2 log 2$
B $log 2$
C $2$
D $1$

Correct answer: D

Solution

(d) We are given that the curve is: e^{y} = 1 + x^{2} \Rightarrow y = log_{e} (1 + x^{2}) Now, m = \frac{dy}{dx} = (\frac{1}{1 + x ^{2}}) \cdot 2 x At x = 1, m = (\frac{1}{1 + 1}) \cdot 2 = \frac{1}{2} \times 2 = 1

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