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1

### IIT-JEE 1996

Fill in the Blanks
If $$x{e^{xy}} = y + {\sin ^2}x,$$ then at $$x = 0,{{dy} \over {dx}} = ..............$$

$$1$$
2

### IIT-JEE 1990

Fill in the Blanks
If $$f\left( x \right) = \left| {x - 2} \right|$$ and $$g\left( x \right) = f\left[ {f\left( x \right)} \right]$$, then $$g'\left( x \right) = ...............$$ for $$x > 20$$

$$1$$
3

### IIT-JEE 1986

Fill in the Blanks
The derivative of $${\sec ^{ - 1}}\left( {{1 \over {2{x^2} - 1}}} \right)$$ with respect to $$\sqrt {1 - {x^2}}$$ at $$x = {1 \over 2}$$ is ...............

$$4$$
4

### IIT-JEE 1985

Fill in the Blanks
If $$f\left( x \right) = {\log _x}\left( {In\,x} \right),$$ then $$f'\left( x \right)$$ at $$x=e$$ is ................

$$1/e$$

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12