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Magazine Problem 108
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=(x-1)(x+1)$$
Problem 109
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\frac{x^{5}-x^{3}}{x^{2}}$$
Problem 110
The population \(P\), in thousands, of a small city is given by \(P(t)=\frac{500 t}{2 t^{2}+9}\) where \(t\) is the time, in years. (GRAPH CANNOT COPY) a) Find the growth rate. b) Find the population after 12 yr. c) Find the growth rate at \(t=12\) yr.
Problem 110
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\frac{5 x^{2}-8 x+3}{8}$$
Problem 111
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\frac{x^{5}+x}{x^{2}}$$
Problem 111
The temperature T of a person during an illness is given by \(T(t)=\frac{4 t}{t^{2}+1}+98.6\) where \(T\) is the temperature, in degrees Fahrenheit, at time \(t,\) in hours. (GRAPH CANNOT COPY)
Problem 112
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\frac{x^{5}-3 x^{4}+2 x+4}{x^{2}}$$
Problem 112
Differentiate each function. \(f(x)=\frac{7-\frac{3}{2 x}}{\frac{4}{x^{2}}+5} \quad(\) Hint: Simplify before differentiating.)
Problem 113
Differentiate each function. $$y(t)=5 t(t-1)(2 t+3)$$
Problem 113
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=(-4 x)^{3}$$
