How to Simplify the Derivative of s=(t2)(1/7)

[Jim4592]

Homework Statement

Find ds/dt for s=(t²)^(1/7)

Homework Equations

I attempted to find the answer by using the chain rule...

The Attempt at a Solution

ds/dt = (1/7)*(t²)^-(6/7)*(2t)
ds/dt = (2/7)*t*(t²)^-(6/7)

I believe that would be the answer but the problem is that the answer key in the book tells me that ds/dt = (2/7)t^-(5/7)

I don't understand what they did to cancel out the t² ang get the power to be -5/7

 

[mplayer]

Simplify 's' first before you take the derivative. Remember the properties of exponents.

 

[Jim4592]

thanks i got it now that i said s=t^(2/7)

 

[Mark44]

Homework Statement

Find ds/dt for s=(t²)^(1/7)

Homework Equations

I attempted to find the answer by using the chain rule...

The Attempt at a Solution

ds/dt = (1/7)*(t²)^-(6/7)*(2t)
ds/dt = (2/7)*t*(t²)^-(6/7)

Your answer is correct, but it's not as simplified as it can be. Also, using the chain rule led to a lot of unnecessary work that could have been avoided by simplifying the expression first.

(2/7)*t*(t²)^-(6/7)
=(2/7) *t* t^-12/7
=(2/7) *t^7/7* t^-12/7
= (2/7) * t^-5/7

I believe that would be the answer but the problem is that the answer key in the book tells me that ds/dt = (2/7)t^-(5/7)

I don't understand what they did to cancel out the t² ang get the power to be -5/7