Home > Calculus > Power Rule

How do you find the derivative of #y =sqrt(9-x)#?

Answer 1

Charles Arocha

First you will rewrite the equation to #y = (9-x)^(1/2)#.

Using the power rule and the constant rule, you then apply the chain rule, which provides you with:

#y'=1/2(9-x)^(-1/2)*-1#

Ultimately, you reduce to:

#y'=-1/2(9-x)^(-1/2)# or #y'= -1/(2sqrt(9-x))#

In order to make the process of finding the derivative easier, you usually start by changing the roots to their exponent forms.

The chain rule, which stipulates the following, must be used when one function is nested inside another:

#F(x)=f(g(x))# then #F'(x)=f'(g(x))*g'(x)#

It's fairly easy to take a derivative using the power rule if:

#f(x) = x^n# then #f'(x) = n*x^(n-1)#. #f(x) = y#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elijah Abram

To find the derivative of ( y = \sqrt{9 - x} ), you can use the chain rule. The derivative is ( \frac{-1}{2\sqrt{9 - x}} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.