Calculus Answers

Use logarithmic differentiation to find the derivative of the function.
y = (tan(x))^(3/x)

Use logarithmic differentiation to find the derivative of the function.
y = x of ln(x)

Find an equation of the tangent line to the curve at the point (1, 1).
y = ln (xex2)

Differentiate the function.
g(x) = ln(x sqrt(x^2 - 7))

Use logarithmic differentiation to find the derivative of the function.
y = sqrt(x)e^x^2(x^2 + 3)^5

Find f '(1).
f(x) = (ln(x)) / x^9

Differentiate the function.
y = 2x log7(√x)

The volume V of a growing spherical cell is given below, where the radius is measured in micrometers (1 µm = 10-6m). Evaluate your answers numerically. (Round the answers to one decimal place.)


(a) Find the average rate of change of V with respect to r when r changes from 5.
(i) 5 to 8 µm µm3 / µm
(ii) 5 to 6 µm µm3 / µm
(iii) 5 to 5.1 µm µm3 / µm

Differentiate the function.f(x) = log[sub]9[/sub](xe[sup]x[/sup])

A manufacturer estimated marginal cost (MC) and marginal revenue (MR) at
various levels of output (q), as seen below:

q(units) 0 20 40 60 80 100 120
MC($per unit) 260 250 240 200 240 250 250
MR($per unit) 410 350 300 250 270 250 240
• Using the trapezoid rule, estimate the revenue and variable production cost
for 100 units.