# Prove that the given series of functions is continuously differentiable. [duplicate]

$f(x)= \Sigma_{n=1}^{\infty} \frac {\sin nx^2}{1+n^3}$, $x\in {\mathbb{R}}$

I can show continuity by using uniform convergence and the Weierstrass M test. But I don't know how to do differentiability. Any help would be highly appreciated. Thank you.

• Is that $f(x)= \Sigma_{n=1}^{\infty} \frac {\sin nx^2}{1+n^3}$ or did I get this wrong? – For the love of maths Jan 18 '18 at 13:15
• @Mohammad Zuhair Khan That's right. – WhySee Jan 18 '18 at 13:17
• Should I edit your question to give the equation in $\LaTeX$ or did you give the image on purpose? – For the love of maths Jan 18 '18 at 13:20
• @Mohammad Zuhair Khan I am using a mobile. So I'm not very comfortable using MathJax on phone. Hence the image. – WhySee Jan 18 '18 at 13:21
• Even me but I think the community in general prefers $\LaTeX$ over images. So, should I edit your question. Takes only $5$ seconds. BTW are you using the app or chrome? – For the love of maths Jan 18 '18 at 13:23