\(\(f(x)=ax^N\)\)¶

\(\(f'(x)=aNx^{N-1}\)\)¶

Section 3.1¶

Examples¶

Problem 1¶

find \(y'\) for \(y=x^{9.2}\) \(y=x^{9.2}\) \(\boxed{y=9.2x^{8.2}}\)

Problem 2¶

find \(f'(x)\) for \(f(x)=\frac{1}{x^{16}}\) \(f(x)=x^{-16}\) \(\boxed{f(x)=-16x^{-17}}\)

Problem 3¶

find \(y'\) for \(y=\sqrt[9]{x}\)

Problem 4¶

find \(f'(x)\) for \(f(x)=x^\pi\) \(f(x)=x^\pi\) \(\boxed{f(x)=\pi x^{\pi-1}}\)

Problem 5¶

find \(f'(t)\) for \(f(t)=7t^2-7t+15\) \(f(t)=7t^2-7t+15\) \(\boxed{f(t)=14t-7+0}\)

Problem 6¶

find \(y'\) for \(y=6t^{15}-12\sqrt{t}+\frac{4}{t}\) \(y=6t^{15}-12\sqrt{t}+\frac{4}{t}\) \(y=6t^{15}-12t^3+4t^{-1}\) \(\boxed{y=90t^{14}-36t^2-4t^{-2}}\)

Problem 7¶

find \(y'\) for \(\sqrt{x}(x^3+7)\) \(\sqrt{x}(x^3+7)\) \(\sqrt{x}(x^3+7)\)

Problem 10¶

On what intervals is the function \(f(x)=x^3-3x^2\) both decreasing and increasing