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Problems 1-5. Differentiate. When appropriate, you might consider first simplifying the expressions before differentiating. For example, n (a*b) = ln a+ln bor n (a^b) = b ln a.

1. (x) = ln root (x+1)with respect to http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bx%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15.

2. (theta) = ln (2 theta)(with respect to heta).

3. (t) = ln root (t^3-6)(with respect to http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bt%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15).

4. (t) = log_2 (sin t)(with respect to http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bt%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15).

5. (x) = ln |x^2-1|)(with respect to http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bx%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15).

6. Let = [ln x]/[e^x]. Find y/dxand d^2y]/[dx^2](the second derivative of ln x]/[e^x]).

7. Find an equation of the tangent line to = ln ln xat the point e,0)(notation: n ln x = ln (ln x). Graph both the function and the tangent line.

8. Use logarithmic differentiation to find x^(3 x))'.

9. Use logarithmic differentiation to find [(-x-4)*(3 x+1)]/[root (5x)] )'.