How do you find the derivative of #y =sqrt(3x+1)#?

Answer 1

It is important to rewrite radicals in rational exponent form when differentiating them:

#y = (3x+1)^(1/2)#

It is now more evident that the derivative of this function can be found by using the power rule first, followed by the chain rule:

#dy/dx = 3*(1/2*(3x+1)^(-1/2))#

All that's left to do is streamline a little bit:

#dy/dx = 3/(2sqrt(3x+1))#

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Answer 2

Charles Anctil

To find the derivative of ( y = \sqrt{3x + 1} ), you can use the chain rule of differentiation. The derivative is ( \frac{dy}{dx} = \frac{1}{2\sqrt{3x + 1}} \cdot \frac{d}{dx}(3x + 1) ). Differentiating (3x + 1) with respect to (x) gives (3). Therefore, the derivative of ( y = \sqrt{3x + 1} ) is ( \frac{1}{2\sqrt{3x + 1}} \cdot 3 = \frac{3}{2\sqrt{3x + 1}} ).

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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.