IIT-JEE 1994 | Differentiation Question 22 | Mathematics

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IIT-JEE 1994

MCQ (Single Correct Answer)

-0.5

If $$y = {\left( {\sin x} \right)^{\tan x}},$$ then $${{dy} \over {dx}}$$ is equal to

$${\left( {\sin x} \right)^{\tan x}}\left( {1 + {{\sec }^2}x\,\log \,\sin \,x} \right)$$

$$\tan x{\left( {\sin x} \right)^{\tan x - 1}}.\cos x$$

$${\left( {\sin x} \right)^{\tan x}}{\sec ^2}x\,\log \,\sin \,x$$

$$\tan x{\left( {\sin x} \right)^{\tan x - 1}}$$

IIT-JEE 1990

MCQ (Single Correct Answer)

-0.5

Let $$f(x)$$ be a quadratic expression which is positive for all the real values of $$x$$. If $$g(x)=f(x)+f''(x)$$, then for any real $$x$$,

$$g(x)<0$$

$$g(x)>0$$

$$g(x)=0$$

$$g\left( x \right) \ge 0$$

IIT-JEE 1988

MCQ (Single Correct Answer)

-0.5

If $${y^2} = P\left( x \right)$$, a polynomial of degree $$3$$, then $$2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^2}}}} \right)$$ equals

$$P''\left( x \right) + P\left( x \right)$$

$$P'\left( x \right)P''\left( x \right)$$

$$P\left( x \right)P''\left( x \right)$$

a constant

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