#### Topic: WHAT IS THIS (Calculus help :( )

"installed" MathJax with a quick hack

AM I RETARDED

\(

\Large x = t^2 + t \)

\( \Large y = \sin t \)

\( \huge \frac{dy}{dx} = \frac{\left( \frac{dy}{dt} \right)}{ \left( \frac{dx}{dt} \right) } = \frac{\cos t}{2t + 1}\)

\(

\huge

\frac{d}{dx} \left( \frac{dy}{dx} \right) =

\frac{d}{dx} \left(\frac{\cos t}{2t+1} \right) = - \frac{ \sin t \cdot \frac{dt}{dx} \cdot \left( 2t + 1 \right) + 2 \cdot \frac{dt}{dx} \cdot \cos t}{\left( 2t + 1 \right) ^2 }

\)

WHAT THE FUCK AM I DOING

This thing is before the section of implicit differentiation... so I don't get how you can take the... SUBSTITUTION, PERHAPS. Hmm. Wait, no. Fuck. I don't get how you can take d/dx of something in terms of something else without implicit differentiation. Fuck.

The book's answer is...

\( \huge \frac{d}{dx} \left( \frac{dy}{dx} \right) = - \frac{\left( 2t + 1 \right) \left( \sin t \right) + 2 \cos t}{\left( 2t + 1 \right) ^3 } \)