Question

Using implicit differentiation find y2 f{d y}{d x} when (x+y)^{5}=sin (y+2 x)

Answer 1

To find y^2 f(d y)/(d x), we need to use implicit differentiation to differentiate the given equation (x+y)^5 = sin(y+2x) with respect to x.

Step-by-step explanation:

To find <em>y² f{d y}{d x}</em>, we need to use implicit differentiation to differentiate the given equation (x+y)&sup5; = sin(y+2x) with respect to x.

Step 1: Differentiate both sides of the equation with respect to x.

(x+y)&sup5; = sin(y+2x)

Using the chain rule, the left side becomes: 5(x+y)&sup4;(1)(1+y') = cos(y+2x)(1+y') + sin(y+2x)(2)

Step 2: Solve for y' by isolating it.

5(x+y)&sup4;(1)(1+y') = cos(y+2x)(1+y') + sin(y+2x)(2)

Now we can substitute for y' to find y² f{d y}{d x}.