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Show that cosh^2(x)-sinh^2(x)=1

In exponential form, sinh^2(x)=1/4(e^2x+e^-2x-2), cosh^2(x)=1/4(e^2x+e^-2x+2). Therefore cosh^2(x)-sinh^2(x)=1/4(2-(-2))=4/4=1, as required.
TD
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Differentiate x^2 + xy + y^2 =1 implicitly.

Each part can be done separately, so x^2 becomes 2x, xy becomes dy/dx + y by product rule, y^2 becomes 2y(dy/dx) by chain rule, and 1 becomes 0. Hence the answer is 2x + y + (2y+1)dy/dx = 0, but the answer i...
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Answered by Tutor80806 D. • Maths tutor
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What is the Electoral College?

The Electoral College (EC) is a constitutional mechanism, better described as a process. It is used to elect the President and Vice-President. The EC was introduced as a compromise between a popular voter by...
SS
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Order the relative base strength of phenyl amine, methyl amine and methylphenyl amine and outline your reasoning.

Phenyl amine is the weakest base- the benzene group has a negative inductive effect on the lone pair on the nitrogen. Therefore it is less availiable for donation. Methyl amine is the strongest- the methyl g...
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Answered by Thomas F. • Chemistry tutor
5320 Views

Differentiate 3x^2+1/x and find the x coordinate of the stationary point of the curve of y=3x^2+1/x

To differentiate we multiply by the power and take one off the power. d/dx(3x^2+1/x)= 6x-1/x^2 At a stationary point the gradient equals zero 6x-1/x^2=0 which rearranges to x=(1/6)^(1/3)
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Answered by Rachel W. • Maths tutor
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