Taking the derivative of a function with a square root in it.

Question

Find the derivative of the given function.
y = (t^(3/2))(22 + √t)

 

So I tried to take the derivative of the function by multiplying t^(3/2) by t^(1/2) and then I got

 

(3/4)t^(-1/4) but it was wrong. Please help me figure out how to take the derivative of the function.

Answer 1

Phil, you are correct that the √t is the same as t^1/2. 

 

The problem is y = (t^3/2) * (22 + t^1/2)

 

Let's multiply thru.

 

y = 22t^3/2 + t²

 

When you multiple like bases, you add the exponents. 3/2 + 1/2 = 4/2 = 2

Answer 2

Rewrite the function so that it contains only exponents.

 

y = t^3/2(22 + t^1/2)

 

 

Distribute the terms to get rid of the parenthesis.

 

y = 22t^3/2 + t²

 

 

Now you can take the derivative of the function using the power rule.