# Questions tagged [derivatives]

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

20,883 questions
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### Derivation,Series,partial derivative! [on hold]

In this question & is a partial derivative. D.D.D=µ[&3-(1/12+1/16)&5+….] HOW IT CAN BE SOLVE.I Am not understanding the basic step how it may proceed
1answer
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### Derivate of absolute value of complex valued function

I have a derivate where $a(z)$ is complex valued. $$\frac{da(z)}{dz}=-\Delta a(z)-\Delta^*e^{-2i\omega z/\bar{c}}b(z)$$ where $\Delta=\frac{\sigma}{2\bar{\zeta}}-\frac{i\omega\nu}{2\bar{c}}$ and star ...
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### Derivative of product and summed function

I am trying to take the derivative with respect to $x$ of the following function: $$F(x) = \sum_{i} ax^i(1-bx^j)\prod_k(1-cx^k)$$ With $i\in [2,n]$, $j=n-i+1$ and $k=i+1$ to $n$. I am struggling ...
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### Derivative of $f(x)=\int_{x}^{\sqrt {x^2+1}} \sin (t^2) dt$

Derivative of $f(x)=\int_{x}^{\sqrt {x^2+1}} \sin (t^2) dt$ Firstly I wanted to calculate $\int \sin (t^2) dt$ and then use $x$ and $\sqrt {x^2+1}$. But this antiderivative not exist so how can I do ...
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### This paper implies that $a \frac{\partial{b^\ast}}{\partial{q}} = b \frac{\partial{a^\ast}}{\partial{q}}$ and I don't see why.

This question is regarding a particular paper that claims a particular result that I cannot seem to follow. The paper is: Cyclic Spectroscopy of the millisecond pulsar, B1937+21 (The paper should be ...
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### Calculating derivative with multiple variables

Let z = f(x,y), x = x(t,s) and y = y(t,s) all be twice continously differentiable functions Try to find $$\frac{\partial z^2}{\partial t^2}$$ I've tried it and only got: \frac{\partial z}{\...