Differentiate... How to solve this type of problem? y = cos^2(x^2 + x^3)

Step-by-step explanation:

Step(i):-

Given y = cos² (x² + x³)  ....(i)

By using differentiation formulas

a)    

b)    

Step(ii):-

    Differentiating equation (i) with respective to 'x'

First apply formula  

Now we will apply formula

Again apply formula  

we know that trigonometric formulas

Sin 2θ  = 2 sinθ cosθ

Final -

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get