# Thread: 2. Differentiate the following function

1. ## 2. Differentiate the following function

f (t) = 1/7t^6-5t^4+9t

2. Do you know the power rule?

$\tfrac{d}{dx} x^n = nx^{n-1}$

3. no, and i have a horrible teacher, can you take me through the steps, please?

4. 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?

5. 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.

6. so is that the way you work out the problem that i'm currently doing because i'm still lost and still confused.

7. 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.

8. (6/7)t^5-20t^3+9t^0 is this right, tell me what i'm supposed to do with the 9t^0

9. 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