Finding dy/dx and the equation of the tangent line

Question

Given the equation below, find dy/dx.

-7x^7+3x^28 y+y^4=-3

*Hint the x^28 are separate from the y so the y isn't included in the exponent.*

dy/dx=

Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx+b format

y=  

Answer 1

-7x⁷ + 3x²⁸y + y⁴ = -3

-49x⁶ + 3(28x²⁷y + x²⁸(dy/dx)) + 4y³(dy/dx) = 0

Since (1,1) is on the curve, -49 + 3(28 + dy/dx) + 4(dy/dx) = 0

So, 7(dy/dx) + 35 = 0. Therefore, dy/dx = -5.

Equation of tangent line: y - 1 = -5(x - 1).

y = -5x + 6