Question

(a) Calculate the derivative of 𝑦=3.4𝑥^(3)−2.8𝑥^(0.5)

(b) Calculate the derivative of cos(𝑥)/𝑥

Answer 1

[AI-generated answer — Bot]

(a) The derivative of 𝑦=3.4𝑥^(3)−2.8𝑥^(0.5) is:

𝑦′ = 10.2𝑥^(2) − 1.4𝑥^(-0.5)

(b) The derivative of cos(𝑥)/𝑥 can be found using the quotient rule:

Let 𝑢 = cos(𝑥) and 𝑣 = 1/𝑥
Then 𝑢′ = -sin(𝑥) and 𝑣′ = -1/𝑥^2

Using the quotient rule, we get:

(𝑐𝑜𝑠(𝑥) 𝑥′ − 𝑐𝑜𝑠′(𝑥) 𝑥)/𝑥^2
= (-sin(𝑥) 𝑥 - cos(𝑥))/𝑥^2
= (-sin(𝑥) / 𝑥) - (cos(𝑥) / 𝑥^2)

Therefore, the derivative of cos(𝑥)/𝑥 is:

𝑐𝑜𝑠(𝑥)/𝑥^2 - 𝑠𝑖𝑛(𝑥)/𝑥