query: Prove the derivative of $f(x)=\left( \left| x \right| \right) ^{3}$ exist.
positive_passages.docid: 17310
positive_passages.text: Can $f(x)=|x|^3$ be differentiated
negative_passages.docid: 93967
negative_passages.text: Prove partial derivatives exist, but not all directional derivatives exists.
negative_passages.docid: 68854
negative_passages.text: Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
negative_passages.docid: 55125
negative_passages.text: Continuous right derivative implies differentiability
negative_passages.docid: 44880
negative_passages.text: Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even.
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 64381
negative_passages.text: Prove that if one of $\lim_{x \rightarrow 0 }{f(x)}$ and $\lim_{x \rightarrow 0}{f(x^3)}$ exists, then the other one also exists.
negative_passages.docid: 115712
negative_passages.text: Application of Derivatives rigorous proof
negative_passages.docid: 99918
negative_passages.text: The $100$th derivative of $(x^2 + 1)/(x^3 - x)$
negative_passages.docid: 53627
negative_passages.text: Proving continuity of $f$
negative_passages.docid: 78834
negative_passages.text: if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
negative_passages.docid: 67853
negative_passages.text: Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
negative_passages.docid: 30204
negative_passages.text: Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
negative_passages.docid: 16109
negative_passages.text: Prove that $ \int _a^b\:f\left(x\right)\:\:dx\:=\:\int _a^b\:f\left(a+b-x\right)\:\:dx $
negative_passages.docid: 146318
negative_passages.text: Derivative of f(x)=arth(lnx)
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 88683
negative_passages.text: Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$