The derivative of cos 2x is -2 sin 2x. The derivative can be written as d(cos 2x)/dx or (cos 2x)'
Calculus is a comprehensive course covering real numbers, functions, and derivatives. Real numbers and lines form the foundation of calculus. Functions can be defined using domain conventions and graphing tools. Trigonometric functions provide basic calculations and applications
States that there exists a point where tangent to arc is parallel to secant. First described by Parameshvara in 1460 for sine interpolation. Modern form proved by Cauchy in 1823
Calculus originated from ancient Egypt and Babylonia with volume calculations. Greek mathematicians like Archimedes developed integral calculus methods. Chinese Liu Hui invented method of exhaustion in 4th century AD. Indian mathematicians like Madhava introduced Taylor series in 14th century
Calculus studies limits, functions, derivatives, integrals, and infinite series. It is a major branch of mathematics used in physics and mechanics. Calculus helps analyze real-world phenomena like business growth and space travel
Double integral computes function integrals over two-dimensional regions. Calculated by integrating inner and outer integrals separately. Requires upper and lower limits of integration