Differentiate
Differentiate the shown equation:
Expand Hint
The power rule for the first derivative:
$$$\frac{d}{dx}[x^n]=n\cdot x^{n-1}$$$
Hint 2
Rewriting the equation:
$$$y=2x^{-3}+9x^{-1}-\frac{2x^5}{5}-10x^{1}-20x^{0}$$$
The power rule for the first derivative:
$$$\frac{d}{dx}[x^n]=n\cdot x^{n-1}$$$
Rewriting the problem statement’s equation to be in the power rule’s format:
$$$y=2x^{-3}+9x^{-1}-\frac{2x^5}{5}-10x^{1}-20x^{0}$$$
Taking the first derivative via power rule:
$$$y'=2(-3)x^{-3-1}+(-1)9x^{-1-1}-\frac{(5)2x^{5-1}}{5}-(1)10x^{1-1}-(0)20x^{0-1}$$$
$$$y'=-6x^{-4}-9x^{-2}-2x^{4}-10x^{0}-0$$$
$$$y'=-6x^{-4}-9x^{-2}-2x^{4}-10$$$
$$$y'=-6x^{-4}-9x^{-2}-2x^{4}-10$$$
Time Analysis
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