Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
 
        
             
        
        
        
646/3=x
To check it: x*3 should =646
        
                    
             
        
        
        
She distributed the 4 to the 2x-1, giving her 9+ 8x -4. she subtracted 8x from both sides leaving her with 4=9-4 which is the same as 4=5
        
                    
             
        
        
        
Answer:
Decimal 0.333 to a fraction in simplest form is:   
Step-by-step explanation:
Given the decimal

Multiply and divide by 10 for every number after the decimal point.
There are three digits to the right of the decimal point, therefore multiply and divide by 1000.
Thus,

           ∵ 0.333×1000 = 333
         ∵ 0.333×1000 = 333
Let us check if we can reduce the fraction 
For this, we need to find a common factor of 333 and 1000 in order to cancel it out.
But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000
<u>Greatest Common Divisor (GCD) : </u>
The GCD of a, b is the largest positive number that divides both a and b without a remainder.
Prime Factorization of 333:      3 · 3 · 37
Prime Factorization of 1000:      2 · 2 · 2 · 5 · 5 · 5
As there is no common factor for 333 and 1000, therefore, the GCD is 1.
Important Tip:
- As GCD is 1, therefore the fraction can not be simplified.
Therefore, decimal 0.333 to a fraction in simplest form is:   
 
        
             
        
        
        
Y would be 16,
y=kx
6=3k
2=k
y=2(8)
y=16