Differentiate $11x^5 + x^4y + xy^5=18$ I am not sure how to differentiate $11x^5 + x^4y + xy^5=18$. I have a little bit of experience with implicit differentiation, but I'm not sure how to handle terms where both variables are multiplied together.
I have tried
$$\frac{d}{dx}(11x^5 + x^4y+xy^5) = \frac{d}{dx}(18)$$
$$\frac{d}{dx}(11x^5)+\frac{d}{dx}(x^4y) + \frac{d}{dx}(xy^5)=0$$
differentiating each term
$$\frac{d}{dx} (11x^5)=11\frac{d}{dy}(5x^4) = 55x^4$$
$$\frac{d}{dx} (x^4y) = [4x^3 \cdot y] + [1 \cdot x^4] = 4yx^3+x^4$$
$$\frac{d}{dx}(xy^5) = [1 \cdot y^5] + [x \cdot 5y^4] = y^5 + 5xy^4$$
finding $\frac{dy}{dx}$
$$\frac{dy}{dx}=\frac{-x}{y} = \frac{-[4yx^3+x^4] + [y^5+5xy^4]}{55x^4}$$
According to the website I'm using, "WebWork", this is wrong.

you actually apply the derivative with respect to the variable $x$ in both members and develop using your knowledge of the product's derivative and chain rule. Note that to calculate implicit derivatives you must think of for example $y = y (x)$. This justifies the passage I marked with (*). For examples $\frac{d}{dx}(y^5)= 5y^4\frac{dy}{dx}$ exactly because $y = y (x)$. Then
$$\frac{d}{dx}(11x^5 + x^4y+xy^5) = \frac{d}{dx}(18)$$
$$\frac{d}{dx}(11x^5)+\frac{d}{dx}(x^4y) + \frac{d}{dx}(xy^5)=0$$
$$(55x^4)+ \left( 4x^3 y + x^4 \frac{dy}{dx} \right) +\left( y^5+5xy^4\frac{dy}{dx}\right) = 0 \,\,\,\,\,\,\,\,\,\,(*)$$ 
$$\left( x^4 \frac{dy}{dx} \right) +\left(5xy^4\frac{dy}{dx}\right) = -55x^4-4x^3 y- y^5$$
$$\left( x^4  +5xy^4\right)\frac{dy}{dx} = -55x^4-4x^3 y- y^5$$
$$\frac{dy}{dx} = \dfrac{-55x^4-4x^3 y- y^5}{\left( x^4  +5xy^4\right)}$$
