The derivative of sin(x)cos(x) is cos^2(x) - sin^2(x). This can also be written as cos(2x).
To find the derivative of sin(x)cos(x), you can use the product rule of derivatives. This rule states that the derivative of two functions multiplied together is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function. In this case, the derivative is sin(x)*(-sin(x)) + cos(x)*(cos(x)), which simplifies to cos^2(x) - sin^2(x).
Finding the derivative of sin(x)cos(x) is important in calculus and physics, as it allows us to analyze and understand the rate of change of a function. It can also be used to solve various problems involving motion, such as finding the velocity or acceleration of an object.
Yes, the derivative of sin(x)cos(x) can be simplified to cos(2x). This is a trigonometric identity that can be derived using double angle formulas.
Yes, you can also use the quotient rule and chain rule to find the derivative of sin(x)cos(x). However, the product rule is the most efficient method in this case.