Differentiation Of Trigonometric Functions — Chapter Summary

The derivative of a function

The derivative of a function is defined as the limit of the difference quotient. For example, d/dx(sin x) = cos x is derived using sin C - sin D = 2 c

Key results include

Key results include: d/dx(sin x) = cos x, d/dx(cos x) = -sin x, d/dx(tan x) = sec²x, d/dx(sec x) = sec x tan x, d/dx(cosec x) = -cosec x cot x, d/dx(c

Using substitution and chain rule

Using substitution and chain rule: d/dx(sin⁻¹x) = 1/√(1−x²), d/dx(cos⁻¹x) = −1/√(1−x²), d/dx(tan⁻¹x) = 1/(1+x²), and similar for others. These are der

The second derivative is the derivative

The second derivative is the derivative of the first derivative. For example, if y = sin x, then dy/dx = cos x and d²y/dx² = −sin x. It helps analyze