 Hello and welcome to the session. Let us discuss the following question. It says find the derivative of the following function The given function is sin x plus cos x upon sin x minus cos x to find the derivative of this function We'll be using quotient rule and the derivative of the function u by v with respect to x is given by v into derivative of u with respect to x minus u into derivative of v with respect to x upon v square. So this knowledge will work as key idea Let us now move on to the solution We have to find the derivative of this function with respect to x. That is d by dx of sin x plus cos x upon sin x minus cos x So for convenience, let's say u is equal to sin x plus cos x and v is equal to sin x minus cos x Now we have to find the derivative of this function that is d by dx of u by v Which is by quotient rule equal to v into d by dx of u minus u into dv by dx upon v square Let us now substitute the values of u and v and this we have v as sin x minus cos x into the derivative of u With respect to x u is sin x plus cos x minus u that is sin x plus cos x into derivative of v v is sin x minus cos x Upon v square v is sin x minus cos x. So it is sin x minus cos x whole square now Again, this is equal to sin x minus cos x into derivative of sin x plus cos x now derivative of sin x is cos x and the derivative of cos x is minus sin x. So this becomes cos x minus sin x plus u that is sin x plus cos x into derivative of sin x minus cos x now derivative of sin x is cos x and derivative of cos x is minus sin x. So minus of minus sin x will become plus sin x upon v square that is sin x plus cos x it's minus minus cos x whole square Which is again equal to taking minus common from this we have minus of cos x minus sin x into cos x minus sin x and here we have minus So we are also we have minus minus sin x plus cos x whole square upon sin x minus cos x whole square and this is again equal to minus of cos x minus sin x whole square minus sin x plus cos x whole square upon sin x minus cos x whole square again equal to minus of Applying the formula of a minus b whole square we have cos square x plus sin square x minus 2 sin x cos x minus Now we are applying the formula of a plus b whole square we have sin square x plus cos square x plus 2 sin x into cos x upon sin x minus cos x whole square Again this is equal to minus of we know that cos square x plus sin square x is 1 so this thing becomes 1 minus 2 sin x cos x minus again sin square x plus cos square x becomes 1 plus 2 sin x cos x upon sin x minus cos x whole square Now we open the brackets So this becomes minus 1 plus 2 sin x cos x minus 1 minus 2 sin x cos x upon sin x minus cos x whole square Now plus 2 sin x cos x gets cancelled with minus 2 sin x cos x and we have minus 2 in the numerator as minus 1 minus 1 is minus 2 upon sin x minus cos x whole square Hence the derivative of the given function is minus 2 upon sin x minus cos x whole square and this completes the question bye for now take care have a good day