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 total nom of  code that can be used is equal to 5+3 = 8

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

The answer is in the image 

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