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If y=log(cosx)sinx, then (dy)/(dx) is eq...

If `y=log_(cosx)sinx,` then `(dy)/(dx)` is equal to

A

`(cotxlogcosx+tanxlogsinx)/(logcosx)^(2)`

B

`(tanxlogcosx+cotxlogsinx)/(logcosx)^(2)`

C

`(cotxlogcosx+tanxlogsinx)/(logsinx)^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`y=log_(cosx)sinx=(logsinx)/(logcosx)`
`implies" "(dy)/(dx)=(cotx.logcosx+logsinxtanx)/((logcosx)^(2))`
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OBJECTIVE RD SHARMA-DIFFERENTIATION-Chapter Test
  1. If y=log(cosx)sinx, then (dy)/(dx) is equal to

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  2. If f(x)=log(e)[log(e)x], then what is f' (e) equal to?

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  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

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  4. sqrt(x+y)+sqrt(y-x)=c , then (d^2y)/(dx^2) equals

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  5. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

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  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

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  7. If f(x) is a polynomial of degree n(gt2) and f(x)=f(alpha-x), (where ...

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  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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  9. If f(x)=(1-x)^(n), then the value of f(0)+f'(0)+(f''(0))/(2!)+...+(f...

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  10. xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

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  11. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

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  14. y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)]

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  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

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  16. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

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  17. If f(x)=10cosx+(13+2x)sinx then f'(x)+f(x)=

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  18. If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (...

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  19. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

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  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

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