Question

Find dy/dx such that x=pi/3
a) csc(pi-x)
b) 2^tanx

Answer 1

d(cos(pi-x))/dx = -sin(pi-x) * d(-x)/dx
=-sin(pi-x)*(-1)
=sin(pi-x)
at x= pi/3
sin(pi-pi/3)=(3^1/2)/2

Answer 2

\[y=2^(tanx)\]

Answer 3

take log both side
log y=tanx log2
dfferentiate
(1/y )*dy/dx=sec^2x * ln2
dy/dx=y *sec^2x * ln2
but y= 2^tanx
dy/dx=(2^tanx)*sec^2x * ln2
at x=pi/3
dy/dx = \[2^\sqrt{3}*2^2 * \ln2\]

Answer 4

\[2.772*2^\sqrt{3}\]