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(1)
y=sinx -cosx
y'=cosx+sinx
y'(π/6) = √3/2 +1/2
(2)
y=3/(5-x) +(1/5)x^2
y'=3/(5-x)^2 +(2/5)x
y'(0) = 3/25
(3)
f(t) = sint/(1+cost)
f'(t)
=[(1+cost).cost + (sint)^2 ]/(1+cost)^2
=(1+cost)/(1+cost)^2
=1/(1+cost)
f'(π/4) = 1/(1+ 1/√2) = √2/(√2+1) = √2.(√2-1) = 2-√2
f'(π/2) = 1/(1+ 0) =1
y=sinx -cosx
y'=cosx+sinx
y'(π/6) = √3/2 +1/2
(2)
y=3/(5-x) +(1/5)x^2
y'=3/(5-x)^2 +(2/5)x
y'(0) = 3/25
(3)
f(t) = sint/(1+cost)
f'(t)
=[(1+cost).cost + (sint)^2 ]/(1+cost)^2
=(1+cost)/(1+cost)^2
=1/(1+cost)
f'(π/4) = 1/(1+ 1/√2) = √2/(√2+1) = √2.(√2-1) = 2-√2
f'(π/2) = 1/(1+ 0) =1
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