 Hi and welcome to the session I am Deepika here. Let's discuss the question, differentiate the function with respect to x. Sine of Ax plus b upon cos of Cx plus d. Let us first understand the quotient root. Derivative of u upon v is equal to derivative of u into v minus u into derivative of v upon v square. This is our question rule. In the above question we will apply the question rule. So this is the key idea behind our question. So let's start the solution. Let y is equal to our given function. Sine of Ax plus b upon cos of Cx plus d. Differentiate both sides with respect to x. By quotient rule we have dy by dx is equal to. Now here u is our sine of Ax plus b and v is cos of Cx plus d. So by quotient rule we have derivative of u by v is equal to derivative of u that is dy dx of sine of Ax plus b into v that is cos of Cx plus d minus u that is sine of Ax plus b into derivative of v that is dy dx of dy by dx is equal to. Here u is our sine of Ax plus b and v is our cos of Cx plus d. So by quotient rule we have derivative of u by v is equal to derivative of u that is dy dx of sine of Ax plus b into v that is into cos of Cx plus d minus u that is sine of Ax plus b into derivative of v that is dy dx of cos of Cx plus d upon v square that is cos square Cx plus d. Now we know that derivative of sine theta is cos theta and derivative of cos theta is minus sine theta. So we have dy by dx is equal to cos of Ax plus b into derivative of Ax that is A into cos of Cx plus d minus sine Ax plus b into minus sine Cx plus d into C upon cos square Cx plus d. So this is equal to A cos Ax plus b into cos Cx plus d plus C sine Ax plus b into sine Cx plus d upon cos square Cx plus d. So this is equal to A cos Ax plus b into cos Cx plus d upon cos square Cx plus d plus C sine Ax plus b into sine Cx plus d upon cos square Cx plus d. So this is equal to, so this is equal to A cos Ax plus b. Now 1 over cos theta is sin theta so we have sin Cx plus d plus C sine Ax plus b. Now sine theta upon cos theta is tan theta and 1 over cos theta is secant theta. So this is tan Cx plus d into secant Cx plus d. Hence the derivative of the given function is A cos Ax plus b into secant Cx plus d plus C sine Ax plus b tan Cx plus d into secant Cx plus d. So this is the answer for the above question. I hope the solution is clear to you. Bye and take care.