# 2. Differentiate the following function

• February 12th 2008, 11:45 AM
plstevens
2. Differentiate the following function
f (t) = 1/7t^6-5t^4+9t
• February 12th 2008, 11:47 AM
TrevorP
Do you know the power rule?

$\tfrac{d}{dx} x^n = nx^{n-1}$
• February 12th 2008, 12:50 PM
plstevens
no, and i have a horrible teacher, can you take me through the steps, please?
• February 12th 2008, 12:53 PM
Pulsar06
Quote:

Originally Posted by plstevens
f (t) = 1/7t^6-5t^4+9t

Well, there's one rule and one property you have to know here. First is the power rule, as described above. Second is the fact that the derivative of x + y is the (derivative of x) + (derivative of y). In other words, differentiate each term separately, then add up all the derivatives at the end. Does this help?
• February 12th 2008, 12:53 PM
TrevorP
Basically take whatever number that the variable is raised to. Multiply it by whatever constant was there before and then subtract 1 from the power.

So:

$\tfrac{d}{dx}x^2 = 2x$
$\tfrac{d}{dx}2x = 2$

$\tfrac{d}{dx}3x^{5.9} = 3 \cdot 5.9 x^{4.9}$

It's like that.
• February 12th 2008, 04:50 PM
plstevens
so is that the way you work out the problem that i'm currently doing because i'm still lost and still confused.
• February 12th 2008, 05:45 PM
Pulsar06
Quote:

Originally Posted by plstevens
f (t) = 1/7t^6-5t^4+9t

First differentiate 1/7t^6 using the power rule (6*1/7t^(6-1), according to the rule), then do the same on -5t^4 and 9t.
• February 12th 2008, 06:23 PM
plstevens
(6/7)t^5-20t^3+9t^0 is this right, tell me what i'm supposed to do with the 9t^0
• February 12th 2008, 07:06 PM
topsquark
Quote:

Originally Posted by plstevens
(6/7)t^5-20t^3+9t^0 is this right, tell me what i'm supposed to do with the 9t^0

What is the value of $t^0$? If that is giving you problems, then consider something more fundamental: What is the value of 3^0? 5^0? 8^0? Plug them into your calculator if you don't remember.

-Dan