Mathematics: Find the derivative of the following function, using the various rules for differentiation

Option A.Step-by-step explanation:there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. Let x and y be the number of stamps of 40 cents and 55 cents respectively. Total number of stamps is 45. So Total cost of stamps is $18.75. So But Krista wrote the system of equations as Krista put 0.40 in the first equation meant for the number of stamps. Krista did not write 0.40 in the second equation meant for the value of stamps. Therefore, the correct option...

Find the derivative of the following function, - id1285344, iilovejohnccena1022

Ответ:

juanitarodriguez

14.03.2022

Mathematics

Simplifying f(x)

will let you avoid using the quotient rule:

$f(x)=\dfrac{2x^4+1}{7x^4}+3\sqrt[3]{x^2}-4x^{-1/4}$
$f(x)=\dfrac27+\dfrac17x^{-4}+3x^{2/3}-4x^{-1/4}$

and now you're just taking derivatives of power functions. You should get

$f'(x)=0-\dfrac47x^{-5}+2x^{-1/3}+x^{-5/4}$

and we can rewrite this as

$f'(x)=-\dfrac4{7x^5}+\dfrac2{\sqrt[3]{x}}+\dfrac1{x^{5/4}}$

even combining into one fraction as

$f'(x)=-\dfrac17x^{-5}\left(4-14x^{14/3}-7x^{15/4}\right)=-\dfrac{4-14x^{14/3}-7x^{15/4}}{7x^5}$