When using the quotient rule, the derivative exists for all values of x for every function is true.
What is quotient rule?
A technique for determining the derivative of a function that is the ratio of two differentiable functions in calculus is known as the quotient rule. Let h(x) = f(x) / g(x), where g(x) ≠ 0 and f and g are both differentiable.
Suppose f(x) and g(x) are the function in variable x.
Is we take the derivative of f(x) and g(x) then both the functions are differentiable.
So, if we apply the quotient rule the functions are differentiable.
And derivative exists for all values of x for both functions f(x) and g(x).
Hence, using the quotient rule, the derivative exists for all values of x for every function.
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