Advanced Mathematics Set 2

Question - 15 Maximum mark : - 30

The derivative of ln (cos x) is:

sec x –sec x –tan x tan x

Find the derivative of arc cos 4x with respect to x.

-4 / [1 – (4x)^2]^2 -4 / [1 – (4x)]^0.5 4 / [1 – (4x)^2]^0.5 -4 / [(4x)^2 – 1]^0.5

Evaluate the first derivative of the implicit function: 4x2 + 2xy + y2 = 0

(4x + y) / (x + y) –[(4x + y) / (x + y)] (4x – y) / (x + y) –[(4x + y) / (x –y)]

Find the derivative of (x + 5) / (x2 – 1) with respect to x.

DF(x) = (-x2 – 10x – 1) / (x2 – 1)2 DF(x) = (x2 + 10x – 1) / (x2 – 1)2 DF(x) = (x2 –10x – 1) / (x2 – 1)2 DF(x) = (-x2 –10x + 1) / (x2 – 1)2

If a simple constant, what is the derivative of y = xa?

a xa – 1 (a – 1)x xa – 1 ax

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