f(x)= 1/4(x^7 - x^3) at x=1
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f(x)= 1/4(x^7 - x^3) at x=1
First, we bring the constant 1/4 out front :
$\displaystyle \frac{1d(x^7-x^3)}{4dx}$
Then, because of the linearity of derivatives:
$\displaystyle \frac{1dx^7}{4dx}-\frac{1dx^3}{4dx}$
Then we apply the power rule twice, resp. for $\displaystyle x^7$ & $\displaystyle x^3$
Thus, the undefined solution is:
$\displaystyle \frac{7x^6}{4}-\frac{3x^2}{4}$
Finally, we fill in $\displaystyle x=1$:
$\displaystyle \frac{7*1^6}{4}-\frac{3*1^2}{4}=\frac{7-3}{4}=\frac{4}{4}=1$
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!