More Derivatives

0. Objective

In this lab we will use Mathematica to explore the derivatives of all of the common functions.  Recall that the D command in Mathematica is used to take the derivative of an expression.

1. Examples

The following are two examples that we have seen formally in class.

D[c,x]

D[Sin[x],x]

Here we see that the derivative of a “constant” is zero and that the derivative of sin(x) is cos(x).

Name:
PIN:

Task

Use Mathematica to evaluate the following derivatives.  Write the results on this sheet next to the function or command:

D[(x^n),x]

D[Cos[x],x]

D[Tan[x],x]

f(x) = sec(x), f’(x) =

g(x) = cot(x), g’(x) =

y=csc(x), (dy/dx)=

D[Log[x],x]

h(x)=(Subscript[log, 5])(x), h'(x)=

w=(2^x), (dw/dx)=

D[3^x,x]

D[f[x]*g[x]*h[x],x]

D[f[g[x]],x]

This last one gives us a way to differentiate composite functions.

z=(Sqrt[(x^2)+5x]), (dz/dx)=

In the following use the Factor, Together and/or Simplify command(s) combined with the below command to find the third derivative

D[((((((x^2)+1))^3)*(((2*x-1))^4))/((((x^4)+16))^6)),{x,3}]