- Take the derivatives of the following functions.
- [latex]f(x) = x^2 e^x[/latex]
[latex]f'(x) = x^2 e^x + 2x e^x[/latex]ans
- [latex]g(x) = \left(\sqrt{x} + 1\right)\left(x^2\right)[/latex]
[latex]g'(x) = \frac{5}{2} x^{3/2} + 2x[/latex]ans
- [latex]h(x) = \frac{1}{x} \left(e^x + 1 \right)[/latex]
[latex]h'(x) = -\frac{1}{x^2} (e^x + 1) + \frac{1}{x} e^x[/latex]ans
- [latex]i(x) = \ln(x) x[/latex]
[latex]i'(x) = 1 + \ln(x)[/latex]ans
- [latex]j(x) = \sqrt{x} \ln(x)[/latex]
[latex]j(x) = \frac{1}{2 \sqrt{x}} \ln(x) + \frac{1}{\sqrt{x}}[/latex]ans
- [latex]m(x) = (x^3 + x^2) \sin(x)[/latex]
[latex]m'(x) = (3x^2 + 2x) \sin(x) + (x^3 + x^2) \cos(x)[/latex]ans
- [latex]l(x) = e^{2x}[/latex] (Hint: You can rewrite this as [latex]e^x \cdot e^x[/latex])
[latex]l'(x) = 2 e^{2x}[/latex]ans
- [latex]\ell(x) = x e^x \ln(x)[/latex]
[latex]\ell'(x) = e^x \ln(x) + e^x \ln(x) + e^x[/latex]ans
- [latex]f(x) = x^2 e^x[/latex]