If derivative of f(x) is f'(x), then what is the integral of (f'(x))^2 in terms of f(x)?
45803
Integral of Derivative squared
100283
How to understand the notion of a differential of a function
135693
Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
3387
Derivative of $f(x)=|x|$
65889
Showing $\Phi(x)=\int_0^x (x-t)f(t)\,dt$ is twice differentiable and finding $\Phi''(x)$
10790
Integration of a function with respect to another function.
104145
Finding the value of $3(\alpha-\beta)^2$ if $\int_0^2 f(x)dx=f(\alpha) +f(\beta)$ for all $f$
1588
How to prove $\int_{-\pi}^\pi (f(x))^2dx\le \int_{-\pi}^\pi (f'(x))^2dx$
84597
Derivative of $(1-x)^{-2}$
104263
How to show that $f'(x)<2f(x)$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
105767
derivative under integral intuition
146888
Derivative of function with 2 variables
25482
If a function is continuous and differentiable everywhere is the derivative continuous?
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
105319
A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$