You can find the derivative of the inverse function by differentiating the inverse explicitly, or by using the formula:

If a function f(x) has an inverse f ⁻¹(x), then by definition

Differentiating both sides with respect to x yields

Now, if f(a) = b and b = f ⁻¹(a), then

Step-by-step explanation:

To find the derivative of inverse hyperbolic function sinh-'(x),

Let

This is an implicit function.  Now differentiate both the sides.

In hyperbolic functions we have relation as

Hence derivative =

Step-by-step explanation:

To find the derivative of inverse hyperbolic function sinh-'(x),

Let

This is an implicit function.  Now differentiate both the sides.

In hyperbolic functions we have relation as

Hence derivative =

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years