Some basic doubts in differentiation

no one?

convert sinx + cosx = √2sin(x + pie/4)

for second ,
see here y is a variable independent of y . If u dont get it den think it in this way . Suppose we put value of x = 0 and y = 3 , the value that we chose of y was independent of the value that we chose for x , it could hav been n e thing. So dy/dx = 0

first of all put x = y

so f(x) [ f(0) - 1 ] = 0

now f(x) = 0 or f(0) = 1

if f(x) = 0 , then f(0) = 0
but f(0) = f'(0)/p ≠0 , since f'(0) cannot be zero since it is in d denominator

so f(0) = 1

so f'(0) = p

now differentiat the given functional eqn wrt x , remembering that y' = 0

so u get f(y)f'(x-y) = f'(x)

put x = y

so f(x)f'(0) = f'(x)

so f(5 ) = f'(5) / f'(0) = q / p