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If sin(x+y)=log(x+y) , then (dy)/(dx)= ...

If `sin(x+y)=log(x+y)` , then `(dy)/(dx)=` (a) 2 (b) -2 (c) 1 (d) `-1]`

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To solve the problem \( \sin(x+y) = \log(x+y) \) and find \( \frac{dy}{dx} \), we will use implicit differentiation. Here are the steps: ### Step 1: Differentiate both sides with respect to \( x \) Given: \[ \sin(x+y) = \log(x+y) \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x...

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  2. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a)1//...

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  3. If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d) -1]

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  4. Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(-1)((2x)/(1-x^2)) , then (d U)...

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  5. d/ dx { tan^ −1 ( cosx/ (1+sinx) ) } equals (a)1/2...

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  6. d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (x^2-1)/(x^2-4) (b) 1 (c) ...

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  7. If y=sqrt(sinx+y) , then (dy)/(dx)= (a)(sinx)/(2y-1) (b) (sinx)/(1-2y...

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  8. If 3sin(x y)+4cos(x y)=5 , then (dy)/(dx)= (a) y/x (b) (3sin(x y)+4co...

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  9. If siny=xsin(a+y) , then (dy)/(dx) is (a)(sina)/(sina sin^2(a+y)) (b) ...

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  10. The derivative of cos^(-1)(2x^2-1) with respect to cos^(-1)x is (a) 2 ...

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  11. If f(x)=sqrt(x^2+6x+9) , then f^(prime)(x) is equal to (a) 1 for x<-3 ...

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  12. If f(x)=|x^2-9x+20| , then f^(prime)(x) is equal to (a) -2x+9 for all ...

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  13. If f(x)=sqrt(x^2-10 x+25) , then the derivative of f(x) in the inte...

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  14. If f(x)=|x-3| and g(x)=fof\ (x) , then for x > 10 , g^(prime)(x) is eq...

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  15. If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l) , th...

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  16. If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a))...

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  17. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2...

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  18. If y=logsqrt(tanx) , then the value of (dy)/(dx) at x=pi/4 is given by...

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  19. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga then (dy)/(dx) is equal to (a)(x...

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  20. If siny=xcos(a+y) , then (dy)/(dx) is equal to (a)(cos^2(a+y))/(cosa) ...

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