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

Answer 1

Deivative of #arcsin(5x+5)# is #5/sqrt(1-25(x+1)^2)#

Let us first find the derivative of #arcsinx# and let #y=arcsinx#,
Then #x=siny# and #(dx)/(dy)=cosy=sqrt(1-sin^2y)=sqrt(1-x^2)#
or #(dy)/(dx)=1/sqrt(1-x^2)# i.e. derivative of #arcsinx# is #1/sqrt(1-x^2)#
Now using chain rule deivative of #arcsin(5x+5)# is
#1/sqrt(1-(5x+5)^2)xx5=5/sqrt(1-25(x+1)^2)#
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Answer 2

To find the derivative of ( y = \arcsin(5x+5) ), you can use the chain rule of differentiation. The derivative is ( \frac{dy}{dx} = \frac{1}{\sqrt{1-(5x+5)^2}} \times (5) ).

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Answer from HIX Tutor

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.

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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