BCA Family An online BCA community

### Derivative

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

1

-2/x2

2/x2

2/x3

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

0

1

2x

-1

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

-12

4

0

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

2

$\sqrt{{x}^{3}}$

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

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

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

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

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

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

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

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 = 0 [2072]

0,2/

2/3

0

-2

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

0

does not exist

2

1

20. The derivative of y = bx is [2071]

xbx-1

b

xbln|b|

bxln|b|

21. The derivative of $y=cos\left(cos\sqrt{x}\right)$ is [2071]

$\frac{sin\left(cos\sqrt{x}\right).sin\left(\sqrt{x}\right)}{2\sqrt{x}}$

$sin\left(cos\sqrt{x}\right)$

$sin\left(sin\sqrt{x}\right)$

$\frac{sin\left(cos\sqrt{x}\right)}{2\sqrt{x}}$

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

1

2

0

1

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

-1

1

6

0

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

5xloge5

5x

loge5

5loge5

I there is