Implicit differentiation \[x^6+y^4=−7\]

To find y' (or dy/dx) through Implicit Differentiation, we need to use the Chain Rule when we see y. While the derivative of x with respect to x is 1, the derivative of y will be y' (or dy/dx) by the Chain Rule. This is where the "respect to" really needs to be observed.

x⁶ + y⁴ = -7

6x⁵ + y⁴ = -7 by taking the derivative of x⁶, using the Power Rule

6x⁵ + 4y³y' = -7 by taking the derivative IMPLICITLY of y⁴ and using the chain rule

6x⁵ + 4y³y' = 0 By taking the derivative of 0

Now we use algebra to get y' alone on one side, and not y' on the other.

6x⁵ + 4y³y' = 0

4y³y' = - 6x⁵

y' = -6x⁵ / 4y³

y' = -3x⁵ / 2y³.

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1