Final answer:
The derivative of the function f(x) = -x + tanx is -1 + sec^2x.
Step-by-step explanation:
In calculus, the derivative of a function measures how the function changes as its input changes. Geometrically, it represents the slope of the tangent line to the graph of the function at a given point. The derivative is a fundamental concept in calculus and has various applications in understanding rates of change, optimization, and physics.
To find the derivative of the function f(x) = -x + tanx, we can use the sum and product rules. The derivative of -x is -1, and the derivative of tanx is sec^2x. Therefore, the derivative of f(x) is -1 + sec^2x.