Find the second derivative of y with respect to x for the following function defined parametrically
x = + 3t + 1
y =  − 3t + 1

Find the second derivative of y with respect to x for the following function defined parametrically
x = a (cos t + t sin t)
y = a (sin t − t cos t)

Find  where x = sec t and y = tan t

Find the derivative  of the following function
x³ + x²y + y² = 0

Find the derivative  of the following function
ln x +  = c

Find the derivative  of the following function
x² + y² – 4x – 10y + 4 = 0

Find the derivative  of the following function
 

Find   if tan⁻¹y – y + x = 0

Find   if = y – x

Find   if x + y = e^{x – y}

Find the value of y” at x = 1 if
x³ – 2x²y² + 5x + y – 5 = 0 and  = 1

a) 5

b) – 8

c)

d)

Find  for the following implicit function
 

Find  for the following implicit function
 = ln

Find  for the following implicit function
sin y − cos x = 0

Find  for the following implicit function
 + xy = e, find  at the point (0, 1)

Find  of the following function
x² + 5xy + y² – 2x + y – 6 = 0
find  at the point (1, 1)

For the following function represented parametrically
 

For the following function represented parametrically find  
x = ln (1 + t²)

y = t −

For the following function represented parametrically
 

For the following function represented parametrically find
 

For the following function represented parametrically find
 

For the following function represented parametrically find
 

For the following function represented parametrically find