 Hello friends, let's work out the following problem. It says find the derivative of the following function The given function is x squared plus 1 into cos x to find derivative of this function will be using product rule It says d by dx of the function u into v is u into dv by dx plus V into d u by dx So this will be the key idea. Let us now move on to the solution We have to find the derivative of the function x squared plus 1 into cos x Now here we'll apply the product rule to find derivative of this function here u is x squared plus 1 and V is cos x So now apply the product rule In the first term u remains as it is so u into dv by dx that is d by dx of cos x Plus and then the second term V remains as it is so here cos x remains as it is into d u by dx Now this is equal to x squared plus 1 Into derivative of cos x derivative of cos x is minus sin x plus cos x Into derivative of x bar plus 1 derivative of x square is 2x as we know that derivative of x to the power n is n into x to the power n minus 1 here n is 2 so it becomes 2 into x to the power 2 minus 1 that is 2x Plus derivative of 1 derivative of 1 is 0 because we know that derivative of constants are 0 So this is equal to minus sin x into x square is minus x square sin x minus sin x minus sin x into 1 is minus sin x Plus 2x into cos x Hence the derivative of the given function is minus x square sin x minus sin x Plus 2x cos x and this completes the question. Bye for now. Take care. Have a good day