Find dy/dx implicitly and find the largest interval of the form −a < y < a or 0 < y < a such that y is a differentiable function of x. cos y = x

dy/dx = -1/√(1 - x²)

For 0 < y < π

Step-by-step explanation:

Given the function cos y = x

-siny dy = dx

-siny dy/dx = 1

dy/dx = -1/siny (equation 1)

But cos²y + sin²y = 1

=> sin²y = 1 - cos²y

=> siny = √(1 - cos²y) (equation 2)

Again, we know that

cosy = x

=> cos²y = x² (equation 3)

Using (equation 3) in (equation 2), we have

siny = √(1 - x²) (equation 4)

Finally, using (equation 4) in (equation 1), we have

dy/dx = -1/√(1 - x²)

The largest interval is when

√(1 - x²) = 0

=> 1 - x² = 0

=> x² = 1

=> x = ±1

So, the interval is

-1 < x < 1

arccos(1) < y < arxcos(-1)

= 0 < y < π

false

step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)