Thread: Differentiating a function?

1. Differentiating a function?

How do I differentiate these functions? I was told I am suppose to multiply the exponent by the variable, then subtract one from the exponent, is this correct? Even if it is correct I am not sure what I am doing wrong.

y = 3x + 2 The answer I got was 5
y = x^2 - 2 Answer I got is 2x - 2
y = x^3 - 2x Answer I got is 3x^2 - 2

Can anyone give me helpful hints as to what I am doing wrong?

2. Only your third answer is correct. Can you show a few more steps for the first two, so I can see exactly what isn't happening correctly?

3. Originally Posted by colerelm1
How do I differentiate these functions? I was told I am suppose to multiply the exponent by the variable, then subtract one from the exponent, is this correct? Even if it is correct I am not sure what I am doing wrong.

y = 3x + 2 The answer I got was 5
y = x^2 - 2 Answer I got is 2x - 2
y = x^3 - 2x Answer I got is 3x^2 - 2

Can anyone give me helpful hints as to what I am doing wrong?
I see what you're doing.

you are not differentiating the constants....

What's the derivative of a constant?

4. The general rule for derivative of a power of x is
$\displaystyle \frac{d x^n}{dx}= n x^{n-1}$

But it is important to note that the "3" in 2x+3 can be thought of as "$\displaystyle 3x^0$ so its derivative is $\displaystyle 3(0x^{-1})= 0$. $\displaystyle 2x= 2x^1$, of course, so its derivative is $\displaystyle 2(1x^0)= 2$. The derivative of 2x+ 3 is $\displaystyle 2(1x^0)+ 3(0x^{-1})= 2+ 0= 2$.

In my opinion, far more important than memorizing a formula like that is knowing that "the derivative is the slope of the tangent line to the graph". Since the graph of y= 2x+ 3 is a line, the derivative is just the slope, 2.

Also important, the derivative is a "rate of change" of the function. A constant function does not change. It's derivative (rate of change) is always 0. In the first and second problems, you differentiated the constants incorrectly.