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Magazine Problem 114
Differentiate each function. $$f(x)=x\left(3 x^{3}+6 x-2\right)\left(3 x^{4}+7\right)$$
Problem 115
Differentiate each function. $$g(x)=\left(x^{3}-8\right) \cdot \frac{x^{2}+1}{x^{2}-1}$$
Problem 115
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\sqrt[3]{8 x}$$
Problem 116
Differentiate each function. $$f(t)=\left(t^{5}+3\right) \cdot \frac{t^{3}-1}{t^{3}+1}$$
Problem 116
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=(x-3)^{2}$$
Problem 117
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}$$
Problem 117
Differentiate each function. $$f(x)=\frac{(x-1)\left(x^{2}+x+1\right)}{x^{4}-3 x^{3}-5}$$
Problem 118
Differentiate each function. Let \(f(x)=\frac{x}{x+1}\) and \(g(x)=\frac{-1}{x+1}\) a) Compute \(f^{\prime}(x)\) b) Compute \(g^{\prime}(x)\) c) What can you conclude about \(f\) and \(g\) on the basis of your results from parts (a) and (b)?
Problem 118
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=(\sqrt{x}+\sqrt[3]{x})^{2}$$
Problem 119
Find \(d y / d x .\) Each function can be differentiated using the rules developed in this section, but some algebra may be required beforehand. $$y=(x+1)^{3}$$
