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Find the derivative with respect to x and the x-coordinate of the stationary point of: y=(4x^2+1)^5

y=(4x^2+1)^5 y=u^5 u=4x^2+1 y’=5u^4 (wrt u) u’=8x y’=40x(4x^2+1)^4 y’=40x(4x^2+1)^4=0 x=0 (x^2+1>0)
EB
Answered by Ellie B. • Maths tutor
4506 Views

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
10951 Views

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...
TD
Answered by Tutor80806 D. • Maths tutor
6194 Views

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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Which conditions led to the collapse of the German war effort in the First World War ?(as is part of the Causes, Practices and Effects of War part of the HL Course)

Outline the four major reasons for the collapse of the German war effort, in a good essay each of these should take up about a paragraph each, with each paragraph following the PEA form (Point, Evidence, Ana...
JW
Answered by Joseph W. • History tutor
2211 Views