- #1

opus

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## Homework Statement

Find the derivative of ##y=cos^3(πx)##

*Must be in Leibniz notation

## Homework Equations

## The Attempt at a Solution

(i) $$Let~ w=y^3 , y=cos(u), u=πx$$

(ii) $$\frac{dw}{dy} = 3y^2,~ \frac{dy}{du} = -sin(u),~ \frac{du}{dx}=π$$

(iii) By the Chain Rule,

$$\frac{dw}{dx} = \frac{dw}{dy}⋅\frac{dy}{du}⋅\frac{du}{dx}$$

(iv) $$= 3cos^2(πx)⋅-sin(πx)⋅π$$

(v) $$=-3πcos^2(πx)sin(πx)$$

I'm not sure if this is correct. We're told to use Leibniz notation, but were taught the Chain Rule in "prime notation", so I just put things together in what made some sort of sense. So I'd like to know if this is correct, and if I'm using this notation correctly.

Thank you for your time.