Use the Chain Rule to find frac(dw)(dt) where w=sin 8x cos 2y, x = frac(t)(2) and y = t^4. (Type an expression using x and y as the variables)

Dottie Parra

Dottie Parra

Answered question

2021-09-09

Use the Chain Rule to find dwdt, where w=sin8xcos2y,x=t2  and  y=t4
dwdx
(Type an expression using x and y as the variables)
dwdy
(Type an expression using x and y as the variables)
dydt
(Type an expression using t as the variable )
dwdt
(Type an expression using t as the variable )

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-09-10Added 109 answers

Step 1
Please see the explanation below
Step 2
w=sin8xcos2y,x=t2  and  y=t4
dwdx=8cos8xcos2y,dwdx=2sin8xcos2y
dydt=4t3,dwdt=dwdxdxdt+dwdydydt
dwdt=(8cos8xcos2y)(12)+(2sin8xcos2y)4t3
=4cos(4t)cos(2t4)8t3sin(4t)cos(2t4)

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