Consider the following. 7/x - 1/y = 6
(a) I solved part a for y' using implicit differentiation, it is y'= (7y²) / (x²)
(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.
(c) Check the consistency of your solutions to part a and b by substituting the expression for y into your solution for part a

B and C are the only ones i'm having trouble with. I know how to do this in general, just that the fractions in this particular case are messing me up, if you could help me that would be much appreciated!

Using differentiation, it is found that:

a)

The implicit derivative is:

b)

The explicit derivative is:

c)

Substituting into part a, we have that:

The expression given is:

Item a:

Applying implicit differentiation, we have that:

Item b:

First, we solve the expression for y, then:

Applying the quotient derivative rule:

Item c:

We have that the expression for the derivative is is:

Substituting into part a, using :

A similar problem is given at link

Solution/answer is in the explanation.

Step-by-step explanation:

Let's check a for fun.

a)

I will rewrite so I can use power rule and chain rule on the first two terms.

Now let's begin.

Let's simplify:

Add on both sides:

Divide both sides by :

Using law of exponents we can rewrite this as:

.

So a) does look good (Great job!).

b)

We need to solve for first since we want to do this explicitly. That is what that means by the way.

Subtract on both sides:

Multiply both sides by :

Multiply both sides by :

Divide both sides by :

Symmetric property:

Multiply the right hand side be :

(the is the explicit equation since it is solved for .

Now we are to differentiate this.

Let's use quotient rule :

c) So we need to see if a) and b) are actually the same now.

For a) we go and we solve for in b) we go .

I'm going to find so I can just replace

Squaring both sides:

I will leave it as this because we may not have to do further work such as expanding the bottom.

Let's plug this into our solution for a):

Division by a number is the same as multiplication by the reciprocal of that number. So let's rewrite:

Now we can cancel the common factor from the top and bottom:

We see this is the same solution we got for b).

We have completed the objective for c).

answer: 2/4

step-by-step explanation:

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !