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 =

The answer is in the image 

The answer is in the image 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

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.