 Hello friends welcome to the session I am Malka and I am going to help you find dy by dx in the following that is sin square y plus cos xy equal to pi. Now let us begin with the solution we are given sin square y plus cos xy equal to pi. Now we will differentiate both sides with respect to x we get dy dx of sin square y plus dy dx of cos xy equal to dy dx of pi. Now we all know that dy dx of x to the power n is equal to nx n minus 1 into dy dx of x and we all know that dy dx of x is equal to 1. Therefore dy dx of x to the power n is equal to nx n minus 1. Similarly now we will differentiate sin square y so we will get n that is to sin y into dy dx of sin y plus dy dx of cos xy is minus sin xy into dy dx of xy equal to dy dx of constant that is pi is 0. Since we know that dy dx of any constant is always 0 this implies 2 sin y. Now dy dx of sin y is cos y into dy by dx minus sin xy. Now we will apply the product rule to dy dx of xy that is first term into derivative of second term plus second term into derivative of first term equal to 0. Here we see that our first term is x so we will find the derivative of second term that is y and our second term is y so we will find the derivative of first term that is x. This implies as we all know that 2 sin y cos y is equal to sin 2y so this can be written as sin 2y into dy by dx minus sin xy into x into dy by dx plus y into dy dx of x is 1 equal to 0. Here we have used the identity that is 2 sin y cos y is equal to sin 2y this implies sin 2y into dy by dx minus sin xy into x into dy by dx minus y into sin xy equal to 0. This implies now we will take dy by dx common of these two terms so we will get dy by dx into sin 2y minus x into sin xy and we will shift this term to r r h so we will get y sin xy. This implies dy by dx equal to y sin xy upon sin 2y minus x into sin xy therefore we can say that dy by dx equal to y sin xy upon sin 2y minus x into sin xy so hope you understood the solution and enjoyed the session. Goodbye and take care.