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How do you find the derivative of #y = arcsin(3x + 4)#?

Answer 1

Emma Aldridge

#y'=3/sqrt(-9x^2-24x-15)#

#y'=1/sqrt(1-(3x+4)^2) *3#-> chain rule

#y'=3/(sqrt(1-(9x^2+24x+16))#->FOIL

#y'=3/sqrt(1-9x^2-24x-16)#->Distribute the negative 1

#y'=3/sqrt(-9x^2-24x-15)#->Combine like terms

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Answer 2

Elijah Abram

To find the derivative of ( y = \arcsin(3x + 4) ), you can use the chain rule. The derivative is given by:

[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - (3x + 4)^2}} \cdot \frac{d}{dx}(3x + 4) ]

After taking the derivative of (3x + 4) with respect to (x), which is simply (3), the expression simplifies to:

[ \frac{dy}{dx} = \frac{3}{\sqrt{1 - (3x + 4)^2}} ]

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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.