Question

find dy/d(theta)
theta=2 ,

if y=sin(pi/(square root(theta^2+5)))

Show steps thanks!!!

Answer 1

dy/dØ = cos(π/√(Ø^2+5) * (-1/2)(Ø^2 + 5)^(-3/2) ) * (2Ø)
=(-πØ/(Ø^2 + 5)^(3/2) * cos(π/√(Ø^2+5)

so when Ø = 2

dy/dØ = ...

You do the button - pushing.
Make sure to set your calculator to RAD

Answer 2

y = sin(π/√(θ^2+5))

weird, but just apply the rules

y = sun(u)
y' = cos(u) u'

u = π/v
u' = -π/v^2 v'

v = √(θ^2+5)
v' = θ/√(θ^2+5)

put it all together and it spells MOTHER. Or, more mathematically,

πθ*cos(π/√(θ^2+5)) / (θ^2+5)^(3/2)

Answer 3

y = sin [ pi*(t^2+5)^-.5 ]

y' = pi [cos pi*(t^2+5)^-.5] * [-.5(2t)](t^2+5)^-1.5

if t = 2

y' = pi {cos pi/ 3} *[-2] [ 1/27 ]

= -(2pi/27) cos (pi/3)
but cos pi/3 = 1/2
so
-pi/27
CHECK MY ARITHMETIC !!!!
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