Mathematics

Mathematics
Mathematical writing is often not immediately understood and takes time and though before comprehension. When reading the mathematical text, the most difficult part is the mathematical formula. This is represented in the form of signs and letter. The letters may be Roman or Arabic, but each has a specific meaning. At the same time, certain combinations represent different meanings as well. Getting to understand the logic behind the formula derivation, proper use and how certain calculations came to require concentration and deeper understanding of the text. It takes me more than three rounds of reading the text for me to intuit and understand it fully. However, I have to make close references now and then until I am well conversant with its use.
Question 1
The chain rule is used for differentiating compositions of functions. This happens when the function contains layers. The chain rule guides that we start with the outer layers leaving the inner layer untouched and then differentiate the inner layers while holding the outer layer. The final answer is the simplified.
Question2
f(x) = cos (x4) f(x)=cosx4derivative of cos=-sin; hence dydx=[dhdx]4×3 where h=x4ddx(cos(h)).d/dx(h)=-sin(x4).4×3= -4x^3sinx4Question 3
G(x) = (cosx)4Let h=x
ggx=4(cosx)3 .-sinx= -4〖(cos⁡x)〗^3 .sin⁡xQuestion 4
Implicit differentiation of x2+y2=8, at points (2,2) and (-2,2)
On differentiating
2xddx+2yddy=ddx8Hence 2x+2yy’ =02x=-2yy’ meaning y’=-x/yAt (2,2) then y’=-22=-1;At (-2,2) then y’=-(-22) =1