New posts in Derivatives

How would you calculate a derivative of $ f(x)= \frac{\sqrt{x+1}}{2-x}$ by the limit definition?

Is it true that $ \lim_{x\to0}\frac{f'\left(x\right)-\frac{f\left(x\right)-f\left(0\right)}{x}}{x}=\frac{f''\left(0\right)}{2} $

Inequality for function of $\arctan(x)$

Linear approximation of $\cos\big(\frac{\pi}{5}+0.07\big)-\cos\big(\frac{\pi}{5}\big)$

Two methods are giving two different answers to the this differential equation : $\frac{dy}{dx}=\frac{1}{2} \frac{d(\sin ^{-1}(f(x))}{dx}$

Proving the integral inequality $2≤\int_{-1}^1 \sqrt{1+x^6} \,dx ≤ 2\sqrt{2} $

Is there a reason it is so rare we can solve differential equations?

Derivative Greater Than 0 Implies One-To-One Function In Neighborhood

If $\lim_{x \to \infty} f(x) - xf'(x)$ exists, does $\lim_{x \to\infty} f'(x)$ exist as well?

Prove that $f(x_0)>\frac{2}{3}$