CSIT 2069 TU Entrance Exam

Derivative

21. $\frac{d y}{d x}$ of $t = x^{2}, y = \frac{1}{t}$ is [2075]

-2/x²

2/x²

2/x³

22. The derivative of x² with respect to -x² is [2075]

-1

21. If x = t + sint, y = 1 - cost then $\frac{d y}{d x}$ is

tant

tan(t/2)

-tant

-tan(t/2)

22. Derivative of cosx w.r.t sinx is

-tanx

tanx

cotx

-cotx

23. The point of inflection of y = x³ - 12x² - 0 is

-12

20. If y = $\sqrt{x + \sqrt{x + \sqrt{x + . . . . .}}}$ then $\frac{d y}{d x}$ = [2073]

$\sqrt{x^{3}}$

$\frac{\sqrt{x}}{2 y - 1}$

$\frac{1}{(2 y - 1)}$

21. if $y = e^{\sqrt{a x^{2} + b}}$ then $\frac{d y}{d x} = 2$ [2073]

$\frac{a x y}{\sqrt{a x^{2} + b}}$

$\frac{a x y}{\sqrt{a x^{2} + b}} e^{\sqrt{a x^{2} + b}}$

$\frac{x}{\sqrt{a x^{2} + b}}$

$e^{\sqrt{a x^{2} + b}}$

24. The critical points for f(x) = x³ - 3x are: [2073]

± 3

± √3

± 1

0, ± √3

21. The value of x for which the function y = x - x² has $\frac{d y}{d x}$ = 0 [2072]

0,2/

2/3

-2

22. the point of inflection for y = x² - 2x [2072]

does not exist

20. The derivative of y = b^x is [2071]

xb^x-1

x^bln|b|

b^xln|b|

21. The derivative of $y = c o s (c o s \sqrt{x})$ is [2071]

$\frac{s i n (c o s \sqrt{x}) . s i n (\sqrt{x})}{2 \sqrt{x}}$

$s i n (c o s \sqrt{x})$

$s i n (s i n \sqrt{x})$

$\frac{s i n (c o s \sqrt{x})}{2 \sqrt{x}}$

22. The value of x for which the derivative of x²+2x+2 is zero is [2071]

23. The point of inflection of the curve x²+3x²-9x+2 is [2071]

-1

7. The derivative of y = 5x with respect to x is equal to [2070]

5xloge5

loge5

5loge5

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Course Content

Colleges

Triton International College

Triton International College

Derivative