#### Chapter 7 Differential Calculus

Section 7.2 Standard Derivatives

# 7.2.4 Exercises

##### Exercise 7.2.7
Find the following derivatives by simplifying the terms of the functions and then applying your knowledge of the differentiation of common functions ($x>0$):
1. $f\left(x\right):={x}^{6}·{x}^{\frac{7}{2}}=$ .
2. $g\left(x\right):=\frac{{x}^{-\frac{3}{2}}}{\sqrt{x}}=$ .
Thus, we have:
1. $f\text{'}\left(x\right)=$ .
2. $g\text{'}\left(x\right)=$ .

##### Exercise 7.2.8
Simplify the terms of the functions and find their derivatives:
1. $f\left(x\right):=2\mathrm{sin}\left(\frac{x}{2}\right)·\mathrm{cos}\left(\frac{x}{2}\right)=$ .
2. $g\left(x\right):={\mathrm{cos}}^{2}\left(3x\right)+{\mathrm{sin}}^{2}\left(3x\right)=$ .
Thus, we have:
1. $f\text{'}\left(x\right)=$ .
2. $g\text{'}\left(x\right)=$ .

##### Exercise 7.2.9
Simplify the terms of the functions and find the derivatives (for $x>0$ in the first part of this exercise):
1. $f\left(x\right):=3\mathrm{ln}\left(x\right)+\mathrm{ln}\left(\frac{1}{x}\right)=$ .
2. $g\left(x\right):={\left(e{}^{x}\right)}^{2}·e{}^{-x}=$ .
Thus, we have:
1. $f\text{'}\left(x\right)=$ .
2. $g\text{'}\left(x\right)=$ .
Enter the exponential functions as exp, for example, enter $e{}^{4{x}^{2}}$ as exp(4*x^2).