Question

Can someone explain how to find the derivative of this function? Picture will be attached

Answer 1

hint:
I can make this variable changes:
\[\begin{gathered}
z = 5x \Rightarrow z = z\left( x \right) \hfill \\
p = \sqrt {\tan z} \Rightarrow p = p\left( z \right) \hfill \\
y = \cos p \Rightarrow y = y\left( p \right) \hfill \\
\end{gathered} \]
so, I can write:
\[\frac{{dy}}{{dx}} = \frac{{dy}}{{dp}} \cdot \frac{{dp}}{{dz}} \cdot \frac{{dz}}{{dx}} = - \left( {\sin p} \right) \cdot \frac{1}{2}\frac{1}{{\sqrt {\tan z} }} \cdot \frac{5}{{{{\left( {\cos z} \right)}^2}}}\]

Answer 2

@Juscallmesteve: Please let us know your status. Need further help with this problem, or are you OK with it now?

Answer 3

sorry about the late response, I have like 4 exams this week and it is pretty crazy.
but yes thank you for the information