# How to find #dy/dx# from #x^2y+3xy^2-x=5#?

##### 2 Answers

#### Explanation:

To solve this, we need to use implicit differentiation.

Since we are finding the derivative in respect to

To start off, we need to use the Product Rule for the first two terms, since there are two variables being multiplied together.

The Product Rule states:

So we can now set it up like this:

Now that we have the derivative, we need to clean up the answer a bit. We need to move each term without the

Now we factor out a

Divide:

There is your answer

# dy/dx = (1 - 2xy - 3y^2)/(x^2 + 6xy) #

#### Explanation:

We have:

# x^2y+3xy^2-x=5 #

Differentiating wrt

# x^2(d/dx y) + (d/dx x^2)y + (3x)(d/dx y^2) + (d/dx 3x)y^2 -d/dx x = d/dx 5 #

# :. x^2(d/dx y) + (2x)y + (3x)(d/dx y^2) + (3)y^2 -1 = 0 #

Then we apply the chain rule to perform the implicit differentiation:

# x^2(dy/dx) + (2x)y + (3x)(2y dy/dx) + (3)y^2 -1 = 0 #

Now, we collect terms and solve for

# (x^2 + 6xy)(dy/dx) = 1 - 2xy - 3y^2 #

# :. dy/dx = (1 - 2xy - 3y^2)/(x^2 + 6xy) #