Differentiation Of Trigonometric Functions

The fundamental derivatives

The fundamental derivatives are: d/dx(sin x) = cos x, d/dx(cos x) = -sin x, d/dx(tan x) = sec²x, d/dx(cot x) = -csc²x, d/dx(sec x) = sec x tan x, d/dx

For composite functions like sin(u)

For composite functions like sin(u), where u = f(x), the derivative is d/dx[sin u] = cos u × du/dx. This extends to all trigonometric functions: d/dx[

Key derivatives include

Key derivatives include: d/dx(sin⁻¹x) = 1/√(1-x²), d/dx(cos⁻¹x) = -1/√(1-x²), d/dx(tan⁻¹x) = 1/(1+x²), d/dx(cot⁻¹x) = -1/(1+x²), d/dx(sec⁻¹x) = 1/(|x|

When differentiating products like x sin

When differentiating products like x sin x, use (uv)' = u'v + uv'. For quotients like sin x/cos x, use (u/v)' = (u'v - uv')/v². These rules combined w

The second derivative d²y/dx² is found

The second derivative d²y/dx² is found by differentiating the first derivative. For trigonometric functions: d²/dx²(sin x) = -sin x, d²/dx²(cos x) = -