Category: Differentiation

Question Number 120452 by john santu last updated on 31/Oct/20 $$Findtheequationofthelinetangenttotheparametric$$$$curvegivenbytheequations\{\begin{array}{l}x={(1+t^3)}^4+t^2\\ y=t^5+t^2+2\end{array}att=1$$ Answered by physicstutes last updated…

Question Number 120322 by sdfg last updated on 30/Oct/20 Commented by TANMAY PANACEA last updated on 30/Oct/20 $$do{x}^{\prime }means=\frac{dx}{dt}pls\dots$$ Commented by Dwaipayan Shikari last…

Question Number 120243 by benjo_mathlover last updated on 30/Oct/20 Answered by bemath last updated on 30/Oct/20 $$letf\left(x\right)=x^{\frac{1}{x^6}}\iff \ln f\left(x\right)=\frac{\ln \left(x\right)}{x^6}$$$$differentiatingbothsidesgives$$$$\frac{{f}\:'\left({x}\right)}{{f}\left({x}\right)}\:=\:\frac{{x}^{\mathrm{5}} −\mathrm{6}{x}^{\mathrm{5}}…

Question Number 54679 by Raj Singh last updated on 09/Feb/19 Commented by maxmathsup by imad last updated on 09/Feb/19 $$letf\left(x\right)=\frac{1}{\sqrt{x+a}}forx>-awehave{f}^{{}^{\prime }}\left(x\right)={lim}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}$$$$={lim}_{{h}\rightarrow\mathrm{0}} \:\:\frac{\frac{\mathrm{1}}{\:\sqrt{{x}+{h}+{a}}\:\:}−\frac{\mathrm{1}}{\:\sqrt{{x}+{a}}}}{{h}}\:={lim}_{{h}\rightarrow\mathrm{0}}…

Question Number 119965 by sdfg last updated on 28/Oct/20 Answered by Dwaipayan Shikari last updated on 28/Oct/20 $$\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dt$$$$\frac{{d}\Gamma\left({x}\right)}{{dx}}=\int_{\mathrm{0}} ^{\infty}…