Find the derivative of the following function.Write the solution of each number

Question

3.f(z) = In|cos5z|

ans. f'(x)= -5 tan 5z

6. y = In √tan x

ans. y' = sec²x/2 tan x

Answer 1

f(z) = ln l cos(5z) l

f'(z) = (cos(5z))' / cos(5z) = -5sin(5z) / cos(5z) = -5tan(5z)

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y = ln√tanx = ln(tanx)^1/2 = (1/2)ln(tanx)

y' = (1/2)[ (tanx)' / tanx ] = (1/2)sec²x / tanx = sec²x / (2tanx)