MATH 1211 Written Assignment Unit 5- University of the people

UNIT 5 WRITTEN

ASSIGNMENT MATH 1211:

CALCULUS UNIVERSITY OF

THE PEOPLE

, 1. Find the derivative for the function
Solution
Looking at the function f(x) = 2ex - 8x
Applying the of exponent derivative and the difference rule to the function
d d d
a x = ax(ln(a)) (f ( x )−g ( x ) ) = f
d g(x)
(x )−
dx dx dx dx

where f(x)=2ex and g(x)=8x.
finding the derivative of the function.
d d d
dx
(2ex - 8x) = (2ex) - dx (8x)
dx
d x d
= 2 dx ex - dx 8

=2ex -8x ln(8)
2. Find the derivative for the function
Solution:
Looking at the function f(z)=z5-ez ln(z)
differentiate both sides of the function with respect to z.
d d
(f ( z ) ) = ( z5−ez ln ( z )) … (1)
dz dz

finding the derivative of the sum of two functions p(x) and q(x) is using the below-
stated formula.
d d d
( p (x )−q ( x ) ) = ( p ( x ))− (q (x ))
dx dx dx

Applying the difference rule of derivatives in equation (1).
d d
f'(z) ( z5 )− ( ez ln ( z ) ) … ( 2)
dz dz

Using the product rule of derivative to find the derivative of the product of two
functions p(z) and q(z)