# Tagged Questions

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### Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
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### How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
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### How can I simplify this implicit equation to an explicit equation

How can I simplify this implicit equation to an explicit equation: Tan[5 y/12] - (7 y/((x)^2 + (y)^2 - (3.5)^2)) == 0 i.e: $y=f(x)$ where $y$ is a explicit ...
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### Solve ODE $d^2u/dx^2 + u/A = 0$

How can I solve following ODE with Mathematical: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ with the conditions: $$\left.\frac{d^2u}{dx^2}\right|_{x=0} = 0,$$ $$u(x=0) = B$$ and ...
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### Implicitly differentiate an equation, then solve the resulting equation

Suppose I have an extremely tedious equation to differentiate and want mathematica to help do the differentiation and solve. Consider a less tedious equation: y (x,z) = sin \left(\frac{1}{x} ...
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### Second derivative implicit differentiation using Wolfram Alpha input?

How would you perform second derivative implicit differentiation using Wolfram Alpha input? The reason that I'm using WA input is that it gives you step-by-step solutions and I'm a first year ...
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### Calculating derivatives of roots of equation

I am interested in calculating how the roots of an equation change as one of the variables does, when the equation is evaluated numerically rather than symbolically. I have edited this code to be ...
Here's a homework problem from the Coursera course Calculus: Single Variable by Robert Ghrist Find the derivative $\frac{dy}{dx}$ from the equation $x \tan y - y^2 \ln x=4$ I wanted to check my ...