Differentiate f(x) = sin(x) + cos(x) with respect to x
A
cos(x) - sin(x)
B
sin(x) - cos(x)
C
-sin(x) + cos(x)
D
cos(x) + sin(x)
Correct Answer: Option A — cos(x) - sin(x)
Explanation:
d/dx[sin(x)] = cos(x) and d/dx[cos(x)] = -sin(x). Therefore the derivative of sin(x)+cos(x) = cos(x)-sin(x). Standard trigonometric derivatives must be memorized for calculus-based competitive exams. These are applied in finding maxima minima rates of change tangent line slopes and in solving differential equations.