 Hi, and welcome to the session. I am Deepika here. Let's discuss the question differentiate cos x cube into sine square x5 with respect to x Now we know that derivative of uv dash that is uv dash is equal to u Into derivative of v plus v into derivative of u. This is our product rule This we will apply to differentiate the above function. So let's start the solution Let y is equal to cos x cube into sine square x5 now here our u is u is cos x cube and v is sine square x5 therefore dy by dx is equal to u That is cos x cube into derivative of v that is Derivates d by dx of sine square x5 plus v sine square x5 Into derivative of u that is d by dx of cos x cube Now this is equal to cos x cube now D by dx of sine square x is to sine x cos x so d by dx of sine square x is for five ways to sine x5 Into cos x5 Cos x5 into derivative of x5. This is 5x4 plus sine square x5 Now derivative of cos x is minus sine x. So therefore D by dx of cos x cube is equal to minus sine x cube Into derivative of x cube. This is 3x square. I hope this step is clear to you Now this is again equal to this is equal to 2 into 5x4. This is 10x4 cos x cube sine 5 Into cos x5 into sine square x5 Into sine x cube. So we have differentiate the given function and our answer is 10x4 sine x5 cos x5 minus 3x square sine square So I hope the question is clear to you. Bye and have a nice day