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What is the derivative of #sqrt(2x)#?

Answer 1

Samantha Adkison

Power rule: #(dy)/(dx)[x^n]=n*x^(n-1)#

Power rule + chain rule: #(dy)/(dx)[u^n]=n*u^(n-1)*(du)/(dx)#

Let #u=2x# so #(du)/(dx)=2#

We're left with #y=sqrt(u)# which can be rewritten as #y=u^(1/2)#

Now, #(dy)/(dx)# can be found using the power rule and the chain rule.

Back to our problem: #(dy)/(dx)= 1/2 * u^(-1/2)*(du)/(dx)#

plugging in #(du)/(dx)# we get:

#(dy)/(dx)= 1/2 * u^(-1/2)*(2)#

we know that: #2/2=1#

therefore, #(dy)/(dx)=u^(-1/2)#

Plugging in the value for #u# we find that: #(dy)/(dx)=2x^(-1/2)#

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Answer 2

Ezra Adams

The derivative of sqrt(2x) with respect to x is (1/sqrt(2x)).

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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.