Calculate and graph derivatives of a polynomial function.

[table][tr][td]1.[/td][td]Enter the function [math]f(x)=2x^3-7x^2+5x-1[/math] into the [i]Input Bar[/i] and press [i]Enter[/i].[/td][/tr][tr][td]2.[/td][td]Enter [math]f'\left(x\right)[/math] into the [i]Input Bar[/i] to compute the derivative of [i]f(x)[/i]. [/td][/tr][tr][td][br][/td][td][b]Note: [/b]You can also use the command [math]Derivative(f)[/math] or the [math]\frac{d}{dx}[/math] key on the virtual keyboard to enter the [i]Derivative[/i] command.[/td][/tr][tr][td]3.[/td][td]To calculate the slope of [i]f(x)[/i] in [i]x = 0[/i] enter [math]f'(0)[/math] into the [i]Input Bar [/i]and press[i] Enter[/i].[/td][/tr][tr][td]4.[/td][td]Compute the second derivative of [i]f(x)[/i] using the command [math]Derivative(f,2)[/math].[/td][/tr][tr][td][/td][td][b]Hint:[/b] You can use the [math]\frac{d}{dx}[/math] key on the virtual keyboard to enter the [i]Derivative[/i] command or enter [math]f''(x)[/math] into the [i]Input Bar[/i].[/td][/tr][/table]

Explore derivatives of further functions and calculate partial derivatives of functions with multiple variables.

[table][tr][td]1.[/td][td]Define the function [math]f(x)=e^{k\cdot x}[/math] for which [i]k[/i] is a constant parameter by entering its equation into the [i]Input Bar[/i].[/td][/tr][tr][td]2.[/td][td]Compute the first derivative of [i]f(x)[/i] by typing [math]f'(x)[/math] into the [i]Input Bar[/i] and pressing [i]Enter[/i].[/td][/tr][tr][td]3.[/td][td]Define the function [math]g\left(x\right)=a\cdot sin\left(b\cdot x+c\right)+d[/math] for which [i]a[/i], [i]b[/i], [i]c[/i] and [i]d[/i] are constant parameters.[/td][/tr][tr][td]4.[/td][td]Compute the first derivative of [i]g(x)[/i] by typing [math]g'\left(x\right)[/math] into the [i]Input Bar[/i] and pressing [i]Enter[/i].[/td][/tr][tr][td]5.[/td][td]Compute the fifth derivative of [i]g(x)[/i] by using the command [math]Derivative\left(g,5\right)[/math].[/td][/tr][tr][td]6.[/td][td]Define the function [i]h(x,y)[/i] with two variables by entering [math]h\left(x,y\right)=x^2\cdot y+x\cdot cos\left(y\right)-y^3\cdot\sqrt{x}[/math] into the [i]Input Bar[/i]. [/td][/tr][tr][td]7.[/td][td]Compute the partial derivative with respect to [i]x[/i] for [i]h(x,y) [/i]by using the command [math]Derivative\left(h,x\right)[/math].[/td][/tr][tr][td]8.[/td][td]Compute the partial derivative with respect to [i]y[/i] for [i]h(x,y) [/i]by using the command [math]Derivative\left(h,y\right)[/math].[/td][/tr][/table]