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Chapter 7: Problem 7
Find the derivative of the function. $$ y=x^{4} $$
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Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=\sqrt{x}(x-2)^{2} $$
Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=\left(x^{2}-2 x+3\right)^{3} $$
Use a graphing utility to graph \(f\) and \(f^{\prime}\) on the interval \([-2,2]\). $$ f(x)=x^{2}(x+1)(x-1) $$
Use a symbolic differentiation utility to find the derivative of the function. Graph the function and its derivative in the same viewing window. Describe the behavior of the function when the derivative is zero. $$ f(x)=\sqrt{\frac{x+1}{x}} $$
Use the General Power Rule to find the derivative of the function. $$ f(t)=\sqrt{t+1} $$
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