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 (ln𝑥)