derivative of y=5xsin^-1 x

Answer 1

To find the derivative of the function y = 5xsin^(-1)(x), we will use the chain rule and the derivative of arcsin(x).

The derivative of arcsin(x) is given by:
d/dx arcsin(x) = 1/√(1 - x^2)

Now, let's use the chain rule to find the derivative of y = 5xsin^(-1)(x):

dy/dx = 5 * (d/dx(x)) * sin^(-1)(x) + 5x * (d/dx(sin^(-1)(x)))

Since d/dx(x) = 1 and d/dx(sin^(-1)(x)) = 1/√(1 - x^2), we can substitute these values into the equation:

dy/dx = 5 * 1 * sin^(-1)(x) + 5x * (1/√(1 - x^2))

Simplifying the equation, we have:

dy/dx = 5sin^(-1)(x) + 5x/√(1 - x^2)

So, the derivative of y = 5xsin^(-1)(x) is 5sin^(-1)(x) + 5x/√(1 - x^2).