p. 50 item 12 is d(ln u)/dx = (1/u) du/dx. Item 14 is d(e^u)/dx = e^u du/dx. Item 11 is log base a, not ln. ln u requires u > 0. The same page states that trigonometric arguments are in radians. The evaluations below are original.
u
Differentiable function of x
lnu
Natural log, u > 0
eu
Exponential
Step-by-step solved example
Evaluate d(ln x)/dx at x = 4, and d(e^{2x})/dx at x = 0.
Tangent to ln x at x = 4 has slope 1/4. The curve is the logarithm, not a stress-strain test.
1. Natural log
u = x, du/dx = 1, so d(ln x)/dx = 1/x. At x = 4 the slope is 1/4.
1/4
2. Exponential
u = 2x, du/dx = 2, so d(e^{2x})/dx = 2 e^{2x}. At x = 0 this is 2(1) = 2.
2
Answer: 1/4 and 2
8 practice questions
0/8 correct
1.d(ln x)/dx at x = 4 is
2.d(e^{2x})/dx at x = 0 is
3.p. 50 item 12 is
4.p. 50 item 14 is
5.On the reals, ln x requires
6.d(ln(3x))/dx for x > 0 equals
7.Trigonometric derivatives on p. 50 use arguments in