Find Devivaties with respect to x:

[tommy2st]

Find Devivaties with respect to x:

1). y=sin(cos(x+3));

2). tan(x+y)=ln x+ 5y.

heres my work...just need a double check

1). y=sin(cos(x+3));

2). tan(x+y)=ln x+ 5y.

1:y = sin(cos(x+3))
y' = cos(cos(x+3))(-sin(x+3))(1)
y' = {-sin(x+3)}{cos(cos(x+3))}

2. Tan(x+y) = lnx+5y
Sec^2(x+y)(1+y') = 1/x + 5yy'
y' = {((1/x))-(Sec^2(x+y))}/(Sec^2(x+y) - 5y)

 

[Klungo]

You messed up in deriving 5y on problem 2. (5y)' = 5y'. Not 5yy'. Everything else prior is correct and so is problem 1.