d/dx ( loge x) ( loga x) =
(1) (1/x) loga x (2) (1/x) logx x (3) (2/x) log x (4) (2/x) loga x Solution: Let y =... View Article
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If y = sec-1 1/(1 – 2x2), then dy/dx =
(1) 1/√(1-x2) (2) 2/√(1-x2) (3) 1/√(1+x2) (4) 2/√(1+x2) Solution: Given y = sec-1 1/(1 – 2x2) Put x = sin... View Article
If y = tan-1 ((√a-√x)/(1 + √(ax)), then dy/dx =
(1) 1/2√x(1+x) (2) 1/√x(1+x) (3) -1/2√x(1+x) (4) none of these Solution: Given y = tan-1 ((√a-√x)/(1 + √(ax)) = tan-1... View Article
[latex]\frac{d}{dx}\left ( \cos^{-1}\sqrt{\frac{1+\cos x}{2}} \right )=[/latex]
(1) 1 (2) 1/2 (3) 1/3 (4) none of these Solution: Let y = cos-1 √(1 + cos x)/2 We... View Article
If [latex]y = \frac{2(x-\sin x)^{\frac{3}{2}}}{\sqrt{x}}[/latex], then dy/dx =
(1) [2(x – sin x)3/2/√x] [(3/2)(1 – cos x)/(1 – sin x) – 1/2x] (2) [2(x – sin x)3/2/√x] [(3/2)(1... View Article
If y = (e2x+ e-2x)/(e2x – e-2x), then dy/dx =
(1) -8/(e2x – e-2x)2 (2) 8/(e2x – e-2x)2 (3) 4/(e2x – e-2x)2 (4) -4/(e2x – e-2x)2 Solution: Given y =... View Article
d/dx {ex log (1 + x2)} =
(1) ex (log (1 + x2) + 2x/(1+x2) ) (2) ex (log (1 + x2) – 2x/(1+x2) ) (3) ex... View Article
If [latex]y=\sqrt{\frac{1+e^{x}}{1-e^{x}}}[/latex], then dy/dx =
(1) ex/(1-ex)√(1-e2x) (2) ex/(1-ex)√(1-ex) (3) ex/(1-ex)√(1+e2x) (4) ex/(1-ex)√(1+ex) Solution: Given y = √(1+ex)/(1-ex) Differentiate w.r.t.x dy/dx = 1/2√(1+ex)/(1-ex) \(\begin{array}{l}\frac{dy}{dx}=\frac{1}{2\sqrt{\frac{1+e^{x}}{1-e^{x}}}}\times \frac{((1-e^{x})e^{x}-(1+e^{x})\times... View Article
If [latex]y=\log x\: e^{(\tan x+x^{2})}[/latex], then dy/dx =
(1) \(\begin{array}{l}e^{(\tan x+x^{2})}(\frac{1}{x}\: + (\sec ^{2}x+x)\log x)\end{array} \) (2) \(\begin{array}{l}e^{(\tan x+x^{2})}(\frac{1}{x}\: + (\sec ^{2}x-x)\log x)\end{array} \) (3) \(\begin{array}{l}e^{(\tan x+x^{2})}(\frac{1}{x}\: +... View Article
Why is chlorine more reactive than iodine
Chlorine is higher up group 7 than iodine. The outer shell of the chlorine is closer to the nucleus and... View Article
What happens when an acid is added to a buffer
When a strong acid like (H3O+) is added to the buffer solution the hydronium ion is consumed by the conjugate... View Article
When was the Heisenberg uncertainty principle developed?
The Heisenberg uncertainty principle was developed by young Werner Heisenberg in February 1927. According to the velocity and the position... View Article
How is the CO2 buffer in the blood?
The by-product of respiration carbon dioxide is mixed with the blood, where it is taken by the red blood cells... View Article
Is HCl and NaOH a buffer?
HCl and NaOH is not a butter solution. If HCl and NaOH are mixed together the acid and the base... View Article
Is milk a buffer
Milk is a butter solution. Buffer capacity is the ability of the milk solution to resist change in the pH... View Article
Is HCl and NaCl a buffer solution
No, HCL and NaCl is not a buffer solution. HCl is a strong acid and NaCl is a salt of... View Article
Which is more reactive benzaldehyde or propanal?
The polarity of the carbonyl group in the benzaldehyde is reduced due to resonance but this resonance effect is not... View Article
Which is more basic amine or alcohol?
Amines are more basic and alcohol is acidic in nature since amines are less electronegative. Amine functional group donates electrons... View Article
Is coal made of hydrocarbons?
Coal is made of hydrocarbons. It is composed mainly of carbon. Coal is used as a fuel and in some... View Article
Is sugar a hydrocarbon?
Sugar is a carbohydrate. Carbohydrates include carbon, hydrogen and oxygen while hydrocarbons have only hydrogen and carbon.
