part 2 of 3\nto find dy/dx = y for x^4 + y^3 = 1, we differentiate both sides of the equation with respect…

part 2 of 3\nto find dy/dx = y for x^4 + y^3 = 1, we differentiate both sides of the equation with respect to x.\non the right - hand side, we have\nd/dx1=\non the left - hand side, we have d/dxx^4 + y^3. we already know that d/dxy^3=3y^2y. for the term x^4, we have\nd/dxx^4=\n

part 2 of 3\nto find dy/dx = y for x^4 + y^3 = 1, we differentiate both sides of the equation with respect to x.\non the right - hand side, we have\nd/dx1=\non the left - hand side, we have d/dxx^4 + y^3. we already know that d/dxy^3=3y^2y. for the term x^4, we have\nd/dxx^4=\n

Answer

Explanation:

Step1: Differentiate constant

The derivative of a constant with respect to any variable is 0. So, $\frac{d}{dx}[1]=0$.

Step2: Differentiate $x^4$

Using the power - rule for differentiation $\frac{d}{dx}[x^n]=nx^{n - 1}$, for $n = 4$, we have $\frac{d}{dx}[x^4]=4x^{3}$.

Answer:

The first blank is 0, the second blank is $4x^{3}$