Fall Break Chain Rule Review AP Calculus Fall Break Chain Rule Review

Calculate the derivative 𝑦= (4 𝑥 2 −5) 4 Calculate the derivative

𝑦 ′ = 32𝑥(4 𝑥 2 −5) 3 Answer

Calculate the derivative f(x)=𝑐𝑜𝑠 (3𝑥+5) Calculate the derivative

f'(x)=−3𝑠𝑖𝑛 (3𝑥+5) Answer

Calculate the derivative 𝑦= 7𝑥 2 −9𝑥+5 𝑥 Calculate the derivative

𝑦′=7−5 𝑥 −2 Answer

Calculate the derivative y= 𝑠𝑖𝑛 3 (5𝑥 −9) Calculate the derivative

𝑑𝑦 𝑑𝑥 = 15𝑠𝑖𝑛 2 (5𝑥 −9)∙cos⁡(5𝑥−9) Answer

Calculate the derivative y= 1 𝑠𝑖𝑛3𝑥 Calculate the derivative

𝑦 ′ =−3 (𝑠𝑖𝑛3𝑥) −2 ∙𝑐𝑜𝑠3𝑥 Answer

Logs Practice

ln 𝑒 6 Evaluate

6 (ln x and e^x are inverses!!) Answer

𝑒 𝑙𝑛4 Evaluate

3ln2 + 2ln 2 – ln 16 Write as a single log

ln 2 Answer

Calculate the derivative f(𝑥)= 4𝑒 𝑥 3 Calculate the derivative

f’(𝑥)= 12𝑥 2 𝑒 𝑥 3 Answer

Calculate the derivative y=𝑙𝑛 4𝑥 2 Calculate the derivative

y'= 2 𝑥 Answer

Calculate the derivative: 1.) y=sin⁡(5𝑥+2) 4 2.) f(x)=4𝑒 𝑠𝑖𝑛5𝑥 3.) g(x)=(𝑙𝑛𝑥)(6𝑥−8) 3 4.) y = 𝑠𝑖𝑛7𝑥 𝑒 𝑥

Calculate the derivative: 1.) y=sin⁡(5𝑥+2) 4 y′=20 (5𝑥+2) 3 𝑐𝑜𝑠 (5𝑥+2) 4

Calculate the derivative: 2.) f(x)=4𝑒 𝑠𝑖𝑛5𝑥 f′(x)=20𝑐𝑜𝑠5𝑥∙𝑒 𝑠𝑖𝑛5𝑥

Calculate the derivative: 3.) y=2 𝑒 𝑥 y′= 𝑙𝑛2∙𝑒 𝑥 2 𝑒 𝑥

Calculate the derivative: 4.) g(x)=(𝑙𝑛𝑥)(6𝑥−8) 3 g′(x)= 1 𝑥 (6𝑥−8) 3 +18 (6𝑥−8) 2 (ln⁡𝑥)