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Category: Differentiation

find-dy-dx-from-equation-xy-3-sec-y-3-1-y-4-

Question Number 120912 by bemath last updated on 04/Nov/20 $$\:\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{from}\:\mathrm{equation}\: \\ $$$$\:\frac{\mathrm{xy}^{\mathrm{3}} }{\mathrm{sec}\:\mathrm{y}−\mathrm{3}}\:=\:\mathrm{1}+\mathrm{y}^{\mathrm{4}} \\ $$ Answered by liberty last updated on 04/Nov/20 $$\mathrm{by}\:\mathrm{implicit}\:\mathrm{differential}\: \\ $$$$\Rightarrow\:\frac{\mathrm{xy}^{\mathrm{3}}…

Show-that-the-function-y-x-5-has-no-derivative-at-x-5-

Question Number 186445 by myint last updated on 04/Feb/23 $$\mathrm{Show}\:\:\mathrm{that}\:\:\mathrm{the}\:\:\mathrm{function}\:\:\mathrm{y}\:=\:\:\mid\:\mathrm{x}\:−\mathrm{5}\:\mid\:\:\mathrm{has}\:\:\mathrm{no}\:\:\mathrm{derivative}\:\:\mathrm{at}\:\:\mathrm{x}\:\:=\:\mathrm{5}. \\ $$ Answered by ARUNG_Brandon_MBU last updated on 04/Feb/23 $${f}\:'\left(\mathrm{5}\right)=\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{f}\left({x}\right)−{f}\left(\mathrm{5}\right)}{{x}−\mathrm{5}}=\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{\mid{x}−\mathrm{5}\mid}{{x}−\mathrm{5}} \\ $$$$\underset{{x}\rightarrow\mathrm{5}^{>} }…

Let-a-gt-0-g-x-n-Z-exp-x-n-2-a-Find-the-Fourier-coefficients-of-g-and-deduce-that-for-x-R-n-Z-exp-pin-2-x-2-x-n-Z-exp-pin-2-x-2-

Question Number 120528 by snipers237 last updated on 01/Nov/20 $${Let}\:\:{a}>\mathrm{0}\:,\:{g}\left({x}\right)=\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\frac{\left({x}−{n}\right)^{\mathrm{2}} }{{a}}\right) \\ $$$${Find}\:{the}\:{Fourier}\:{coefficients}\:{of}\:\:\:{g} \\ $$$${and}\:{deduce}\:{that}\:{for}\:{x}\in\mathbb{R}^{\ast} \\ $$$$\:\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\frac{\pi{n}^{\mathrm{2}} }{{x}^{\mathrm{2}} }\right)=\:{x}\:.\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\pi{n}^{\mathrm{2}} {x}^{\mathrm{2}} \right) \\…

Question-186027

Question Number 186027 by Michaelfaraday last updated on 31/Jan/23 Answered by qaz last updated on 31/Jan/23 $$\frac{{d}\mid{y}\mid}{{dx}}=\begin{vmatrix}{\mathrm{sin}\:{x}}&{\mathrm{sin}\:{x}}\\{−\mathrm{sin}\:{x}}&{−\mathrm{sin}\:{x}}\end{vmatrix}+\begin{vmatrix}{\mathrm{cos}\:{x}}&{\mathrm{cos}\:{x}}\\{\mathrm{cos}\:{x}}&{\mathrm{cos}\:{x}}\end{vmatrix}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…

Find-the-equation-of-the-line-tangent-to-the-parametric-curve-given-by-the-equations-x-1-t-3-4-t-2-y-t-5-t-2-2-at-t-1-

Question Number 120452 by john santu last updated on 31/Oct/20 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{tangent}\:{to}\:{the}\:{parametric} \\ $$$${curve}\:{given}\:{by}\:{the}\:{equations}\:\begin{cases}{{x}=\left(\mathrm{1}+{t}^{\mathrm{3}} \right)^{\mathrm{4}} +{t}^{\mathrm{2}} }\\{{y}={t}^{\mathrm{5}} +{t}^{\mathrm{2}} +\mathrm{2}}\end{cases}\:{at}\:{t}=\mathrm{1} \\ $$ Answered by physicstutes last updated…

find-the-point-on-the-curve-3x-2-4y-2-72-closest-to-line-3x-2y-1-0-

Question Number 120378 by john santu last updated on 31/Oct/20 $${find}\:{the}\:{point}\:{on}\:{the}\:{curve}\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} =\mathrm{72} \\ $$$${closest}\:{to}\:{line}\:\mathrm{3}{x}+\mathrm{2}{y}−\mathrm{1}=\mathrm{0} \\ $$ Commented by bramlexs22 last updated on 31/Oct/20 $${let}\:\left({x},{y}\right)\:{is}\:{a}\:{point}\:{on}\:{hyperbola}…