Question

Given 7x^3 * eʸ = 6y³ * 12, compute dy/dx:

(a) y = 42x² * eʸ
(b) y = 14x² / eʸ
(c) y = 6y³ / 7x³
(d) y = 6x² * eʸ

Answer 1

To compute dy/dx in the given equation, differentiate both sides with respect to x, apply the chain rule, and isolate dy/dx.

Step-by-step explanation:

To compute dy/dx in the given equation, we need to differentiate both sides of the equation with respect to x. Let's start with the left-hand side:

d(7x^3 * e^y)/dx = 7 * d(x^3)/dx * e^y + 7x^3 * d(e^y)/dx

Using the chain rule, we have:

7 * 3x^2 * e^y + 7x^3 * e^y * dy/dx = 6y^3 * 12

Simplifying, we get:

21x^2 * e^y + 7x^3 * e^y * dy/dx = 72y^3

Now, let's isolate dy/dx:

7x^3 * e^y * dy/dx = 72y^3 - 21x^2 * e^y

dy/dx = (72y^3 - 21x^2 * e^y) / (7x^3 * e^y)