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How do I simplify a fraction with surds on the bottom when the surd is part of a function?

When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √ 3" was the denominator of the fraction (on th...
CW
Answered by Charlotte W. • Maths tutor
8355 Views

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
4556 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
11078 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
6273 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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