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I do not understand the concept of differential enter image description here for example

What have both the sides been differentiated by to get this result.I understand that dz^2/dz gives 2z,where has the extra dz come from also what has the side with theta been differentiated by to get this result,it cannot be dz.If its dtheta how can you differentiate something with respect to another thing in two sides of an equation.Can someone explain this and how did dz and dtheta come in the equations.

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From the equation you have shown it looks like $z$ depends on $\theta$, so they have differentiated both sides with respect to $\theta$ and then multiplied both sides by $d\theta$.

To differentiate the left hand side you need to use the chain rule since you are differentiating with respect to $\theta$, not $z$.

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  • $\begingroup$ Can you show you can i do that $\endgroup$
    – Naruto
    Commented Jun 4, 2020 at 9:13
  • $\begingroup$ The chain rule states that if a quantity $z$ depends on another quantity $\theta$ and $z$ undergoes some transformation $g$ (in your case $g(z) = z^2$), then the result of differentiating $g(z)$ is $\frac{dg}{dz} \cdot \frac{dz}{d\theta}$ $\endgroup$
    – user794008
    Commented Jun 4, 2020 at 9:21

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