Find dy/dx by implicit differentiation

Question

x^3y^3+y cos x = 5?

Answer 1

The function is x³y³ + y cos(x) = 5.

Differentiate with respect to x.

(d/dx)[x³y³ + y cos(x)] = (d/dx)(5)

[3x³y²y' + 3y³x²] + [-y sin(x) + cos(x)y'] = 0

3x³y²y' + cos(x)y' = y sin(x) - 3y³x²

[3x³y² + cos(x)]y' = y sin(x) - 3y³x²

y' = [y sin(x) - 3y³x²]/[3x³y² + cos(x)].