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Business Calculus
2. Derivatives
2.10 Derivative of inverse trigonometric functions
Derivative of inverse trigonometric functions
What You'll Learn
Derive the formulas for derivatives of inverse sine, cosine, and tangent functions
Apply the chain rule to differentiate inverse trigonometric functions with composite arguments
Use implicit differentiation and Pythagorean identities to prove derivative formulas
Recognize when to apply product and quotient rules with inverse trig functions
Convert between inverse trig notation (arcsin vs sin¹) for differentiation
What You'll Practice
1
Finding derivatives of arcsin, arccos, and arctan with variable expressions inside
2
Applying chain rule to expressions like arctan(e^x) and arccot(3x+1)
3
Using product and quotient rules with inverse trigonometric functions
4
Proving derivative identities involving inverse trig functions
Why This Matters
Inverse trigonometric derivatives are essential for solving integrals, optimization problems, and differential equations in calculus. You'll use these formulas throughout engineering, physics, and advanced mathematics courses whenever angles need to be recovered from ratios.
Before You Start — Make Sure You Can:
This Unit Includes
7 Video lessons
Practice exercises
Learning resources
Skills
Inverse Trigonometric Functions
Chain Rule
Implicit Differentiation
Pythagorean Identity
Product Rule
Quotient Rule
Derivatives
