which of the following functions is not differentiable at x = 0?

Question

a. f(x) = sqrt(x)

b. f(x) = e^x

c. g(x) = tan x

d. f(x) = arcsin x

Answer 1

The derivative of sqrt(x) is 1/(2sqrt(x)). At x = 0, the derivative = 1/(2sqrt0) = 1/0 (undefined)

The derivative of e^x is e^x. At x = 0, the derivative = e^0 = 1

The derivative of tan x is sec^2x. At x = 0, the derivative =sec^2(0) = 1^2 = 1

The derivative of arcsin x = 1/sqrt(1-x^2). At x = 0, the derivative = 1/sqrt(1-0^2) = 1.

Since the derivative for a is undefined for sqrt(x), the function is not differentiable at x = 0.