3.5 – Derivative of Trigonometric Functions REVIEW: Function Notation 𝑦=𝑓(𝑥) 𝑢=𝑓(𝑥) 𝑣=𝑔(𝑥) 𝑠=𝑠(𝑡) Derivative Notation 𝑦 ′ = 𝑓 ′ 𝑥 = 𝑑𝑦 𝑑𝑥 = 𝑑 𝑑𝑥 𝑓 𝑥 = 𝑑 𝑑𝑥 𝑦= 𝐷 𝑥 𝑓 𝑥 = 𝐷 𝑥 𝑦 𝑢 ′ = 𝑓 ′ 𝑥 = 𝑑𝑢 𝑑𝑥 = 𝑑 𝑑𝑥 𝑓 𝑥 = 𝑑 𝑑𝑥 𝑢= 𝐷 𝑥 𝑓 𝑥 = 𝐷 𝑥 𝑢 𝑣 ′ = 𝑔 ′ 𝑥 = 𝑑𝑣 𝑑𝑥 = 𝑑 𝑑𝑥 𝑔 𝑥 = 𝑑 𝑑𝑥 𝑣= 𝐷 𝑥 𝑓 𝑥 = 𝐷 𝑥 𝑣 𝑠 ′ = 𝑠 ′ 𝑡 = 𝑑𝑠 𝑑𝑡 = 𝑑 𝑑𝑡 𝑠(𝑡) = 𝑑 𝑑𝑡 𝑠= 𝐷 𝑡 𝑠 𝑡 = 𝐷 𝑡 𝑠

3.5 – Derivative of Trigonometric Functions Derivative of Sine Derivative of Cosecant 𝑦=𝑓 𝑥 = sin 𝑥 𝑦=𝑓 𝑥 = csc 𝑥 𝑦 ′ = 𝑓 ′ 𝑥 = 𝑑𝑦 𝑑𝑥 = cos 𝑥 𝑦 ′ = 𝑓 ′ 𝑥 = 𝑑𝑦 𝑑𝑥 =−𝑐𝑜𝑡𝑥 𝑐𝑠𝑐𝑥 Derivative of Cosine Derivative of Secant 𝑦=𝑓 𝑥 = cos 𝑥 𝑦=𝑓 𝑥 = sec 𝑥 𝑦′=𝑓′ 𝑥 = 𝑑𝑦 𝑑𝑥 =− sin 𝑥 𝑦′=𝑓′ 𝑥 = 𝑑𝑦 𝑑𝑥 = tan 𝑥 sec 𝑥 Derivative of Tangent Derivative of Cotangent 𝑦=𝑓 𝑥 = tan 𝑥 𝑦=𝑓 𝑥 = cot 𝑥 𝑦′=𝑓′ 𝑥 = 𝑑𝑦 𝑑𝑥 = 𝑠𝑒𝑐 2 𝑥 𝑦′=𝑓′ 𝑥 = 𝑑𝑦 𝑑𝑥 =− 𝑐𝑠𝑐 2 𝑥

3.5 – Derivative of Trigonometric Functions

3.5 – Derivative of Trigonometric Functions

3.5 – Derivative of Trigonometric Functions Practice Problems – Worksheet Derivatives of Trigonometric Functions

3.6 – The Chain Rule Review of the Product Rule: 𝑦= 3 𝑥 3 +2 𝑥 2 2 𝑦= 3 𝑥 3 +2 𝑥 2 2 = 3 𝑥 3 +2 𝑥 2 3 𝑥 3 +2 𝑥 2 𝑦′= 3 𝑥 3 +2 𝑥 2 9 𝑥 2 +4𝑥 + 9 𝑥 2 +4𝑥 3 𝑥 3 +2 𝑥 2 𝑦′=2 3 𝑥 3 +2 𝑥 2 9 𝑥 2 +4𝑥 𝑦= 6 𝑥 2 +𝑥 3 = 6 𝑥 2 +𝑥 6 𝑥 2 +𝑥 6 𝑥 2 +𝑥 𝑦 ′ = 6 𝑥 2 +𝑥 6 𝑥 2 +𝑥 12𝑥+1 + 6 𝑥 2 +𝑥 12𝑥+1 6 𝑥 2 +𝑥 + 12𝑥+1 6 𝑥 2 +𝑥 6 𝑥 2 +𝑥 𝑦 ′ = 6 𝑥 2 +𝑥 2 12𝑥+1 + 6 𝑥 2 +𝑥 2 12𝑥+1 + 6 𝑥 2 +𝑥 2 12𝑥+1 𝑦′=3 6 𝑥 2 +𝑥 2 12𝑥+1

3.6 – The Chain Rule 𝑦= 3 𝑥 3 +2 𝑥 2 2 𝑦′=2 3 𝑥 3 +2 𝑥 2 9 𝑥 2 +4𝑥 𝑦= 3 𝑥 3 +2 𝑥 2 2 𝑦′=2 3 𝑥 3 +2 𝑥 2 9 𝑥 2 +4𝑥 𝑦= 6 𝑥 2 +𝑥 3 𝑦′=3 6 𝑥 2 +𝑥 2 12𝑥+1 Additional Problems: 𝑦= 𝑥 3 +2𝑥 9 𝑦′= 9 𝑥 3 +2𝑥 8 3 𝑥 2 +2 𝑦= 5𝑥 2 +1 4 𝑦′= 4 5𝑥 2 +1 3 10𝑥 𝑦= 2𝑥 5 −3 𝑥 4 +𝑥−3 13 𝑦′= 13 2𝑥 5 −3 𝑥 4 +𝑥−3 12 10𝑥 4 −12 𝑥 3 +1

Practice Problems – Worksheet 3.6 – The Chain Rule Practice Problems – Worksheet The Chain Rule