Question

If sin(x + y)= log(x+y), then dy/dx​

Answer 1

Answer:

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

Answer 2

Answer:

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

so answer is -1