Step 1:
Start by putting [tex] \frac{d}{dx} [/tex] in front of each term
[tex] \frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2][/tex]
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Step 2:
Deal with the terms in 'x' and the constant terms
[tex] \frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2] [/tex]
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Step 3:
Use the chain rule for the terms in 'y'
[tex] \frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx} [/tex]
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Step 4:
Use the product rule on the term in 'x' and 'y'
[tex](y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}
[/tex]
[tex]y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx} [/tex]
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Step 5:
Rearrange to make [tex] \frac{dy}{dx} [/tex] the subject
[tex]-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx} [/tex]
[tex]cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y) [/tex]
[tex][cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y) [/tex]
[tex] \frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y} [/tex] ⇒ Final Answer
