# `f(x) = sqrt(x + 5sin(x)), x<=20` Use a computer algebra system to graph `f` and to find `f'`

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Expert Answers

tiburtius | Certified Educator

We will solve the problem using Wolfram Mathematica (you can also use Wolfram Alpha which is free).

**Graph of **

*Plot[Sqrt[x + 5 Sin[x]], {x, -6, 20}]*

By writing the above line of code we obtain the graph of shown in the image below.

**Finding **

*Simplify[D[Sqrt[x + 5 Sin[x]], x]]*

In the code line above command *Simplify* is there to simplify the result obtained by differentiation.

The result is `(1 + 5 cos(x))/(2 sqrt(x + 5 sin(x)))`

Student Comments

scisser | Student

Graph

Plot is from `(0,20)`

Find the derivative

`f'(x)=(5cos(x)+1)/(2sqrt(x+5sinx))`