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If Sin(x+y)=Log(x+y) then find dy/dx

If Sin(x+y)=Log(x+y)


then find dy/dx

Grade:11

4 Answers

G Narayana Raju
51 Points
9 years ago

-1

Gaurav P
34 Points
9 years ago

is the answer -1?

Sankhadeep Bhattacharya
16 Points
9 years ago

Sin(x+y)=log(x+y)

Þ   d/dx{sin(x+y)}=d/dx{log(x+y)}

Þ   Cos(x+y)(1+dy/dx)=1/x(1+dy/dx)

Þ   Cos(x+y)(1+dy/dx) - 1/x(1+dy/dx)=0

Þ   (1+dy/dx){ Cos(x+y) – 1/x}=0

Þ   It implies (1+dy/dx)=0

Þ   dy/dx=-1

Neeraj Lamba
28 Points
2 years ago
 
    Sin(x+y)=log(x+y) .  Then dy/dx =??
 Step:-1.
      d/dx[sin(x+y)]=d/dx[log(x+y)]
 Step:-2.
      cos(x+y)[1+dy/dx]=1/(x+y)[1+dy/dx]
Step:-3.
     cos(x+y)+cos(x+y).dy/dx=1/(x+y)+1/(x+y).dy/dx
Step:-4.
    cos(x+y)+cos(x+y).dy/dx-1/(x+y)-1/(x+y).dy/dx=0
Step:-5.
  cos(x+y)[1+dy/dx]-1/(x+y)[1+dy/dx]=0
Step:-6.
  cos(x+y)-1/(x+y)[1+dy/dx]=0
     
                 It is evident from above statement that cos(x+y)-1/(x+y) can be equal to zero but [1+dy/dx] can't be equal to zero.
Hence,
 
         1+dy/dx=0
       ____________
         dy/dx=-1        This is the Answer.....
       ____________

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