Question

Differentiate with respect to ( x: cos^2(x) + sin^2(x) ).

A. ( 0 )
B. ( 1 )
C. ( -2sin(x)cos(x) )
D. ( 2sin(x)cos(x) )

Answer 1

Differentiating the expression cos²(x) + sin²(x) with respect to x results in 0 because cos²(x) + sin²(x) equates to the constant 1, according to the Pythagorean identity, and the derivative of a constant is always 0.

Step-by-step explanation:

The question asks to differentiate the expression cos²(x) + sin²(x) with respect to x. This is a common expression in trigonometry, known as the Pythagorean identity, which states that for any angle x, cos²(x) + sin²(x) = 1. Since the derivative of a constant is zero, the derivative of this expression is also zero. Therefore, the correct answer is A. ( 0 ).

To show this step-by-step:

1. Recognize that cos²(x) + sin²(x) = 1 by the Pythagorean identity.
2. Take the derivative of the constant 1 with respect to x, which is 0.