# Are there any functions which are unable to be differentiated?

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As in, say I had a function #f(x)# , and the derivative #f'(x)# . Is there any function for #f(x)# where the equation for #f'(x)# cannot be worked out using any differentiation rules and instead have to be done graphically.

As in, say I had a function

Perhaps this is the kind of thing you're wondering about.

Graphical techniques are only as accurate as our ability to graph and read the graph.

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Yes, there are functions that are unable to be differentiated. These functions typically exhibit certain properties that make them non-differentiable at certain points or over certain intervals. Examples include functions with sharp corners, cusps, or vertical tangents, such as the absolute value function ( |x| ) at ( x = 0 ). Additionally, functions that have discontinuities or behave irregularly can also be non-differentiable.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the derivative of #f(x)=1/(x-1)# using the limit process?
- How do you use the definition of the derivative to differentiate the function #f(x)= 2x^2-5#?
- How do you find f'(x) using the definition of a derivative for #f(x)=(2-x)/(2+x) #?
- How do you find the equation of the line tangent to #f(x)=2x^2# at x=-1?
- What is the slope of the line normal to the tangent line of #f(x) = secx+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?

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