Derivative of a Reciprocal of a Cube Root Function with Chain Rule

This is an excerpt of a class lecture in which I worked an example that used the Chain Rule to find the derivative of the reciprocal of a cube root function. The steps included rewriting the function as a quantity raised to a negative power, then using the special case of the Chain Rule called the General Power Rule to take the derivative. The focus of the video is on how to use the Chain Rule and General Power Rule, not on the theory behind them. This is a Calculus 1 level explanation.

[gabrielrivasmolina]

Gabriel rivas
Mac2311
I learned how to solve the derivate of a cube root function and even when it is in the denominator. Very good explained step by step. Thank you for the video!

[gabrielacaraballo]

Gabriela Caraballo
MAC2311 MTWR12:30
"The chain rule fixes that for us because basically what it says is: you treat this as you would have if it said x^-1/3, but then to compensate for the fact that it wasn't x^-1/3, you multiply times the derivative of the inside part."

[marvindavis]

Marvin Davis
MAC2311 MTWR 12:30
"The chain rule fixes that for us because basically what it says is: you treat this as you would have if it said x^-1/3, but then to compensate for the fact that it wasn't x^-1/3, you multiply times the derivative of the inside part."

[robertogarrido]

Roberto Garrido
MAC2311 MTWR 12:30
1:12 "The Power Rule: Take the power out front and subtract one from it."
1:45 "y prime is going to be the derivative of the outside multiplied by the derivative of the inside."

[robertcasanova]

Robert Casanova
MAC 2311
This video helped me understand how to take a function inside a root of any kind and convert into a form where the chain rule can be applied to find its derivative.

[chantalamsel]

Hi Ms. Hearn. How do I find the derivative of cube root of (x-3)^2 ?

[marialialcantara]

Mariali A.(Mac2311)
In this video I learned, to take the derivative of a cube root function, it is better to rewrite it as a power of 1/3 or in this case to the power of -1/3 since it was in the denominator and we're trying to get it as close as possible to a familiar concept.

[Sophia-]

Sophia Cury MTWR 12:30
1:36 "To compensate for the fact that it wasn't x to the one-third, you multiply by the derivative of the inside part."

[kornikamakeup]

Yonacary Wingard
MAC2311
One thing i learned from this video is how to properly identify when a function can be simplified algebraically before attempting to differentiate. Thank you.

[laurenstofsky]

Lauren Stofsky
MAC2311 MTWR12:30
"the chain rule fixes that for us because basically what it says is you treat this as you would have if it said X to the negative 1/3 but then to compensate for the fact that it wasn't X to the 1/3 you multiply times the derivative of the inside part"

[chrismalliakis]

Chris Malliakis
MAC2311 MTWR 12:30
"7x minus 4 to the negative 1/3 power now we just have a quantity to a power instead of quotient"

[anthonypierredavid]

Anthony David
MAC2311 MTWR 12:30
"To compensate for the fact that it wasn't x to the one-third, you multiply by the derivative of the inside part."

[donna]

Donna Soto
MAC2311 MTWR 12:30
" Now this particular composition of functions involved an exponent, it involved using the power rule and so it comes up so often that this special case of the chain rule has its own name and it's called The General Power Rule"

[clarasaintilien]

Clara Saintilien
MAC2311 MTWR 12:30
"Anytime I see a cubed root, I rewrite it as a power before I even think about what rules I'm gonna use because I know I don't have any rules for roots."

[rafisanchez]

Rafhaela Sanchez
MAC2311 MTWR 12:30
"To compensate for the fact that it wasn't x to the one-third, you multiply by the derivative of the inside part."

[jeremycallaway]

Jeremy Callaway
MAC2311 MTWR 12:30
"In my mind, I know how to take the derivative of a power. The problem is that this rule only applies when the base is just x, not when the base is (7x-4)."

[maeganstofsky]

Maegan Stofsky
MAC2311 MTWR 12:30
"Basically what it says is you treat this as you would have if it said x to the negative 1/3"

[brandonn]

Brandon Nandlal
MAC2311
One thing I liked about the video was avoiding to use the quotient rule since it was only term at the top so you brought it to the top with a negative exponent, thus finding the derivative would be less complicated.

[sallyselevan]

Sally Selevan
MAC2311 MTWR12:30
1:18 "In my mind, I know, I know how to take the derivative of a power. The problem is that this rule only applies when the base is just x, not when the base is 7x-4."

[sermonsermon]

Hi Ms. Hearn. thank you for explaining the use of the general power rule to solve a cube root problem. Sabrine Charles MAC2311 M-TH 2pm