Question

Hi can someone please help me with the following two questions thanks. It is about calculus. Maybe if you show me the steps for the first one i can attempt the second.

Answer 1

both require the chain rule

Answer 2

the derivative of secant is secant times tangent and the derivative of \(\sqrt[3]{x}\) is \(\frac{1}{3\sqrt[3]{x^2}}\)

Answer 3

your answer is therefore
\[\sec(\sqrt[3]{x})\tan(\sqrt[3]{x})\times \frac{1}{3\sqrt[3]{x^2}}\]

Answer 4

isn't the derivative of \[\sqrt[3]{x}\] is 1/3x^(2/3) thanks

Answer 5

yes that is what i wrote too
most times exponential notation is handy but if you want to evaluate anything you really need the radical notation

Answer 6

oh ok thanks hahah

Answer 7

yw

Answer 8

i will attempt the second one now

Answer 9

k
you need the chain rule three twice for that one
recall \(4\cos^3(\pi x)\) really means \(4\left(\cos(\pi x)\right)^3\)

Answer 10

ok thanks

Answer 11

@satellite73

Answer 12

yes, and the final answer is \(-12~\pi~ sin(\pi x)~cos^2(\pi x)\)

Answer 13

because \(\dfrac{d}{dx}x =1\)

Answer 14

is their a simpilar was to do it? or a different way? thanks

Answer 15

ok thanks but maybe u didn't understand me .. i just want to make sure i didn't skip steps or unknowingly used wrong connotations. even if there is a better way to re-arrange the method i used properly. Since i have to show full work. thanks