Tutor profile: Amy M.
Find the derivative. f(x)=(x^6+2)/x
There are two ways to approach this problem. One can either use the quotient rule or separate into two fractions and proceed by just using the power rule. In this case, the second approach makes more sense use. So first step is separating this one fraction into two, so f(x)=(x^6/x) +(2/x) then simplify to get f(x)=x^5+2/x. Rewrite 2/x as 2*x^-1 to make finding the derivative easier. Using the power rule we find that f'(x)=5x^2-(2/x^2).
Find f'(2) if f(x)=ln(x).
First take the derivative of f(x). The derivative of ln(x) is 1/x, so f'(x)=1/x. Now plug in your value of x, which in this problem is 2. So f'(2)=1/2.
Solve for t: 8^t=10 Round to three decimal places.
The first step to solving this problem is taking the natural log of both sides. So you will get ln(8^t)=ln(10). The ln(8^t) can be rewritten as t*ln(8). So we get t*ln(8)=ln(10). Divide both sides by ln(8) to solve for t. Now t=ln(10)/ln(8). Plug this into a calculator to solve and get a final answer of t=1.107.
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