(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find d^{2}y/dx^{2}for cos y + x^{2}=12

The first derivative I think is correct but the second I am unsure of, this is Q5 of 10 in an assignment and every other question has been far cleaner and easier making me think that I've missed something.

We dont have to use implicit differentiation, I thought that it would be easiest though.

thanks for any future help.

2. Relevant equations

3. The attempt at a solution

cos y=x-12

d/dx cos y = d/dx(12-x^{2})

dy/dx=-sin y = -2x

dy/dx=2x*cosec(x)

The first differential is easy, it gets messy from here.

d^{2}y/dx^{2}=d/dx*dy/dx

=d/dx 2x (sin y)^{-1}

=2/(sin y) +2x d/dx (sin y)^{-1}-product

=2/(sin y) +2x [dy/dx -d/dy(sin y)^{-1}]

=2/sin y = (-4x^{2}cos y)/(sin y)^{2}

=2 cosec y + -4x^{2}cot y cosec^{2}y

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Implicit differentiation - Help

**Physics Forums | Science Articles, Homework Help, Discussion**