 Hello students, let's solve the following question. It says find the derivative of the following function. The given function is ax squared plus sin x into p plus q cos x. Here, a, p, q are fixed non-zero constants. To find the derivative of this function, we'll be using product rule. It says d by dx of the function u into v is given by u into dv by dx plus u v into du by dx. So this will be the key idea. Let us now proceed on with the solution. We have to find derivative of ax squared plus sin x into p plus q cos x. Now here we'll use the product rule. Here u is ax squared plus sin x and v is p plus q cos x. Now, by the product rule, u remains as it is here in the first term. This ax squared plus sin x into d by dx of v, that is p plus q cos x plus and in the second term, v remains as it is. That is p plus q cos x into derivative of u. u is ax squared plus sin x. Again, this is equal to ax squared plus sin x. Into d by dx of p. Here p and q are constants plus q into d by dx of cos x plus p plus q cos x into d by dx of ax squared plus d by dx of sin x. Now this is equal to ax squared plus sin x into d by dx of p is 0 because derivative of a constant is 0 and derivative of cos x is minus sin x. So this becomes minus q sin x plus p plus q cos x into derivative of ax squared is 2 ax because 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 ax and a remains as it is because it's a constant plus derivative of sin x and we know that derivative of sin x is cos x. So this is equal to ax squared plus sin x into minus q sin x plus p plus q cos x into 2 ax plus cos x. Hence the derivative of the given function is minus q sin x into ax squared plus sin x plus p plus q cos x into 2 ax plus cos x. And this completes the question. Bye for now. Take care. Have a good day.