# Tagged Questions

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

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### Find $f(x)$, when $\left[f''(x)\right]^2\cdot f(x)=\left[f'(x)\right]^3,\ \forall x\in[0,1]$

Let $f:[0,1]\to\mathbb{R}$ be a twice differentiable function with $f''(x)>0,\ \forall x\in[0,1]$, $f(0)=f'(0)=1$ and $\left[f''(x)\right]^2\cdot f(x)=\left[f'(x)\right]^3,\ \forall x\in[0,1]$....
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### Problem on integration: $\int\frac{\log_{\ e}[\sec x]}{\sqrt{1-x^2}}dx$

Well, Today I am very confused over a integral problem and I tried wolfram and many websites they did not help me. Compute: $$\int\frac{\log_{\ e}[\sec x]}{\sqrt{1-x^2}}dx$$ this I have to solve to ...
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### gateaux derivative and frechet derivative

In calculus, we have the following equation $DF(x,y)=\partial F_xdx+\partial F_ydy$ if $F$ is differentiable. I think such equation still holds for frechet derivative, but not for gateaux derivative. ...
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