# How do you find the derivative of #arcsin(5x)#?

After substitution,

Reverse the substitution

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To find the derivative of ( \arcsin(5x) ), you can use the chain rule.

The derivative of ( \arcsin(u) ) is ( \frac{1}{\sqrt{1-u^2}} ) where ( u = 5x ).

So, the derivative of ( \arcsin(5x) ) with respect to ( x ) is ( \frac{1}{\sqrt{1-(5x)^2}} \times 5 ).

Simplifying, this becomes ( \frac{5}{\sqrt{1-25x^2}} ).

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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.

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