# Thread: What is the derivative?

1. ## What is the derivative?

f(x)= 1/4(x^7 - x^3) at x=1

Thanks

2. ## Common derivative rules

f(x)= 1/4(x^7 - x^3) at x=1

First, we bring the constant 1/4 out front :
$\frac{1d(x^7-x^3)}{4dx}$

Then, because of the linearity of derivatives:
$\frac{1dx^7}{4dx}-\frac{1dx^3}{4dx}$

Then we apply the power rule twice, resp. for $x^7$ & $x^3$

Thus, the undefined solution is:
$\frac{7x^6}{4}-\frac{3x^2}{4}$

Finally, we fill in $x=1$:
$\frac{7*1^6}{4}-\frac{3*1^2}{4}=\frac{7-3}{4}=\frac{4}{4}=1$

I recommend you to take a look at the common rules for derivatives. If you still have any problems, you can always ask them here . Have fun finding derivatives!