Question

if y +x = sin(y+x)^m+n, then dy/dx=​

Answer 1

Answer:

Step-by-step explanation:

$y+x=t\\differentiate\:wrt\:x\\ \frac{dy}{dx}+1=\frac{dt}{dx}\\y+x=sin^{m+n}(y+x)\\t=sin^{m+n}t\\differentiate\:wrt\:t\\ \frac{dt}{dx}=(m+n)sin^{m+n-1}t\:cost\\\frac{dy}{dx}+1=(m+n)sin^{m+n-1}t\:cost\\Therefore\\\frac{dy}{dx}=(m+n)sin^{m+n-1}t\:cost-1$

hope it helps