Calc 1 Derivative Questions?

Question

1. g(x)= cosh(lnx) 

2. y= xcoth(1+x^2) 

3. y=cosh^-1(sqrtx) 

4. y= xtanh^-1x + ln sqrt (1-x^2)

Answer 1

1.

The function is 

g(x)= cosh(lnx) 

It's derivative g '( x) = sinh(ln x) / x .

Answer 2

2.

y= x coth(1+x^2) 

It's derivative y ' 

From the formula d/dx (u v ) = u v' + v u'

y ' = x  [d/dx ( coth(1+x^2))] + coth(1+x^2) (1)

y' = x [-cosec h²(1 +x²) ] (2 x) + Coth(1+x^2)

y' = - 2 x² Cosech²(1 +x² ) +  Coth(1+x^2) .

Answer 3

3.

The function is  y= cosh^-1(sqrtx) 

It' s derivative  y ' is

Hence the derivative of the function is . 

Answer 4

4.

The function is 

It's derivative y' is