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DifferentiationQuestion and Answers: Page 1

Question Number 197664 Answers: 0 Comments: 1

Question Number 197317 Answers: 0 Comments: 0

if x = ((cos θ)/u) , y = ((sin θ)/u) and z = f(x,y) then show that (∂^2 z/∂x^2 ) + (∂^2 z/∂y^2 ) = u^4 (∂^2 z/∂u^2 ) + u^3 (∂z/∂u) + u^4 (∂^2 z/∂θ^2 )

$$\:\mathrm{if}\:\:\:\mathrm{x}\:\:=\:\:\frac{\mathrm{cos}\:\theta}{\mathrm{u}}\:\:,\:\mathrm{y}\:\:=\:\frac{\mathrm{sin}\:\theta}{\mathrm{u}}\:\:{and}\:\mathrm{z}\:\:=\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{u}^{\mathrm{2}} }\:+\:\mathrm{u}^{\mathrm{3}} \:\frac{\partial\mathrm{z}}{\partial\mathrm{u}}\:+\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\theta^{\mathrm{2}} } \\ $$

Question Number 197277 Answers: 1 Comments: 0

Question Number 197057 Answers: 3 Comments: 2

Question Number 196902 Answers: 1 Comments: 0

Question Number 196691 Answers: 0 Comments: 2

Can someone recommend Calculus book , But I prefer if the book isn't boring and have a real challenging problems not a direct consequence of what is illustrated

$$ \\ $$Can someone recommend Calculus book , But I prefer if the book isn't boring and have a real challenging problems not a direct consequence of what is illustrated

Question Number 196628 Answers: 0 Comments: 0

inf ∅ =^? +∞ and sup ∅ =^? −∞

$${inf}\:\varnothing\:\overset{?} {=}\:+\infty\:\:\:\:{and}\:\:\:\:\:{sup}\:\varnothing\:\overset{?} {=}\:−\infty \\ $$

Question Number 196408 Answers: 2 Comments: 0

Calcul ∫^( +∞) _( 0) ((lnt)/( (√t)(1+t^2 )))dt

$$\mathrm{Calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{t}}\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)}\mathrm{dt} \\ $$

Question Number 196401 Answers: 3 Comments: 0

if y=sin x find (d^2 /dy^2 )cos^7 x

$$\mathrm{if}\:{y}=\mathrm{sin}\:{x}\: \\ $$$$\mathrm{find}\:\frac{\boldsymbol{{d}}^{\mathrm{2}} }{\boldsymbol{{d}}{y}^{\mathrm{2}} }\mathrm{co}\boldsymbol{{s}}^{\mathrm{7}} \boldsymbol{{x}} \\ $$

Question Number 196209 Answers: 2 Comments: 0

Ω= ∫_0 ^( 1) (( (x−1)^( 2) )/(ln^2 (x))) dx= ? −−−−

$$ \\ $$$$\:\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({x}−\mathrm{1}\right)^{\:\mathrm{2}} }{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}\:{dx}=\:? \\ $$$$\:\:\:\:\:−−−− \\ $$

Question Number 195952 Answers: 2 Comments: 0

Ω = Σ_(m=1) ^∞ Σ_(n=1) ^∞ (((−1)^( n+1) )/(m^2 n + mn^( 2) )) = ? −−−−−

$$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{n}+\mathrm{1}} }{{m}^{\mathrm{2}} {n}\:+\:{mn}^{\:\mathrm{2}} }\:\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:−−−−− \\ $$

Question Number 195885 Answers: 2 Comments: 0

(dy/dx) + (√((1−y^2 )/(1−x^2 ))) = 0

$$\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\sqrt{\frac{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:=\:\mathrm{0}\: \\ $$

Question Number 195878 Answers: 0 Comments: 0

Question Number 195180 Answers: 1 Comments: 0

1. f(x)= { ((sinx , (π/2)<x≤2π)),((cosx , 0≤x≤(π/2))) :} then find the f^′ ((π/2)) =? 2. f(x)= { ((sinx , (π/2)<x≤2π)),((cosx , 0≤x≤(π/2))) :} then find the f′(2π) =?

$$ \\ $$$$\mathrm{1}.\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}^{'} \left(\frac{\pi}{\mathrm{2}}\right)\:=? \\ $$$$\mathrm{2}.\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}'\left(\mathrm{2}\pi\right)\:=? \\ $$$$ \\ $$

Question Number 195170 Answers: 2 Comments: 0

f(x)= { ((x^7 +2x+1 ;x≥2)),((x^2 +7x+4 ;x<1)) :} f^′ (1)=?

$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{7}} +\mathrm{2}{x}+\mathrm{1}\:\:\:\:\:\:\:;{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{4}\:\:\:\:\:\:\:\:;{x}<\mathrm{1}}\end{cases} \\ $$$${f}^{'} \left(\mathrm{1}\right)=? \\ $$

Question Number 195137 Answers: 1 Comments: 0

f(x)=arctan(((4sinx)/(3+5cosx))) then f^′ ((π/3))=?

$${f}\left({x}\right)={arctan}\left(\frac{\mathrm{4}{sinx}}{\mathrm{3}+\mathrm{5}{cosx}}\right)\:\:\:{then}\:{f}^{'} \left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$

Question Number 194852 Answers: 1 Comments: 0

lim_(x→0) (cosx)^(log(x)) =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\mathrm{log}\left(\mathrm{x}\right)} =? \\ $$$$ \\ $$

Question Number 194467 Answers: 2 Comments: 0

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