Problems 1-5. Differentiate. When appropriate, you might consider first simplifying the expressions before differentiating. For example, n (a*b) = ln a+ln b
or 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/dx
and d^2y]/[dx^2]
(the second derivative of ln x]/[e^x]
).
7. Find an equation of the tangent line to = ln ln x
at 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)] )'
.