If y = log ( sec e x 2 ) , then d y d x =

Question

If $y = \log (\sec e^{x^{2}}),$ then $\frac{d y}{d x} =$

Smart Achievers · Accepted Answer

(3)

Ans. $2 x e^{x^{2}} t a n e^{x^{2}}$

Explanation:

$y = \log (se c e^{x^{2}})$

$\frac{d y}{d x} = \frac{d \log (\sec e^{x^{2}})}{d (\sec e^{x^{2}})} \times \frac{d (\sec e^{x^{2}})}{d (e^{x^{2}})} \times \frac{d (e^{x^{2}})}{d (x^{2})} \times \frac{d (x^{2})}{d x}$

$= \frac{1}{\sec e^{x^{2}}} \times \sec e^{x^{2}} \tan e^{x^{2}} \times e^{x^{2}} \times 2 x$

$∴$ $\frac{d y}{d x} = 2 x e^{x^{2}} \tan e^{x^{2}}$

Solution

Q.
If $y = \log (\sec e^{x^{2}}),$ then $\frac{d y}{d x} =$

1 $x^{2} e^{x^{2}} \tan e^{x^{2}}$

2 $e^{x^{2}} \tan e^{x^{2}}$

3 $2 x e^{x^{2}} \tan e^{x^{2}}$

4 $x e^{x^{2}} \tan e^{x^{2}}$

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Solution

Q. If y=log(sec ex2), then dydx=

1 x2ex2tanex2

2 ex2tanex2

3 2xex2tanex2

4 xex2tanex2