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Derivatives of Trig Functions – 13-Slide Lesson

Derivatives of the six trig functions in a 13-slide PowerPoint: sin x and cos x are derived from the limit definition, tan x from the quotient rule, and the rules for cot x, sec x and csc x are stated.
Derivatives of Trig Functions – 13-Slide Lesson preview: 13-slide editable PowerPoint lesson
Derivatives of Trig Functions – 13-Slide Lesson preview

Look Inside · 10 pages

Lesson cover introduces the objective: calculate derivatives of sine, cosine, tangent, cotangent, secant, and cosecant
Opening slide and lesson objective
Derivative rule review slide covers constant, constant multiple, sum or difference, product, quotient, and chain rules
Review of six differentiation rules
Sine derivative preparation slide shows two trigonometric limits, their graphs, and the sine addition identity
Limits and identity for the sine derivation
Sine derivative derivation uses the limit definition, expands sin(x + h), and simplifies to d/dx sin(x) = cos(x)
Deriving the sine derivative from limits
Cosine derivative derivation rewrites cos(x) as sin(x + π/2) and applies the chain rule to obtain −sin(x)
Deriving the cosine derivative
Tangent derivative derivation applies the quotient rule to sin(x)/cos(x), then simplifies to sec²(x)
Deriving the tangent derivative
Trigonometric derivative summary slide lists formulas for sine, cosine, tangent, cotangent, secant, and cosecant
Summary of all six trigonometric derivatives
Worked examples 1–2 differentiate sin(x) + cos(x) and 3sec(x) − 10cot(x), showing the resulting derivatives
Examples 1–2: sums and constant multiples
Worked examples 3–4 differentiate cos(t²) using the chain rule and 3x⁻⁴ − x²tan(x) using the product rule
Examples 3–4: chain and product rules
Worked example 5 rewrites 1/tan(x) as (tan x)⁻¹ and applies the chain rule to find the derivative −csc²(x)
Example 5: differentiating reciprocal tangent
File type
Microsoft PowerPoint
Use
Digital activity

Updated Oct 19, 2026

Subject
Maths
Topic
Calculus, Derivative
Resource types
Lesson Plans
Use
Digital activity

From the author

About this resource

PowerPoint presentation, 13 slides explaining how to calculate the derivative of the trigonometric function: sin x, cos x tan x, cot x, sec x and csc x.

In the classroom

Teaching tips & learning objectives

Learning objectives

  • Differentiate sin x, cos x, tan x, cot x, sec x and csc x

  • Combine trig derivatives with the product and chain rules

  • Find a tangent line to a trigonometric curve

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Resource details

Concepts & topics

Core concepts

  • Trigonometric derivatives

  • Limit definition of the derivative

  • Quotient rule

Topics

Calculus Derivative Trigonometric Functions Explanation of Derivatives of Trigonometric Functions