Question

derivative of 1/sqrt(x^3 + 1)

please show all work

thanks in advance

Answer 1

\[\large{\frac{d}{dx}{(\frac{1}{\sqrt{x^3+1}})}}\]

Answer 2

Use the chain rule here

Answer 3

do u know about chain rule @JayCT ?

Answer 4

no can you help me pls

Answer 5

Use the chain rule like this
\[\large{\frac{d}{dx}(\frac{1}{\sqrt{x^3+1}})=\frac{d}{du}\frac{1}{\sqrt{u}}\frac{du}{dx}, \space \text{where} u = x^3 + 1\space \text{and} \space \frac{d}{du}{\frac{1}{\sqrt{u}} = \frac{-1}{2u^{\frac{3}{2}}}}}\]

Answer 6

choose quotient rule or pure chain rule... chain rule requires a re-write to push the denominator to the numerator.

Answer 7

so what we get now is :
\[\large{\frac{\frac{d}{dx}(x^3+1)}{2(x^3+1)^{\frac{3}{2}}}}\]

Differentiate the sum term by term :

\[\large{\implies -\frac{\frac{d}{dx}x^3+\frac{d}{dx}(1)}{2(x^3+1)^{\frac{3}{2}}}}\]
Since the deriviateive of a constant = 0

Answer 8

therefore we get :
\[\large{\frac{-\frac{d}{dx}x^3}{2(x^3+1)^{\frac{3}{2}}}}\]
\[\large{\frac{-3x^2}{2(x^3+1)^{\frac{3}{2}}}}\]

Answer 9

got it?

Answer 10

This is much complicated... .

You must be able to know what is :

Chain rule and how to use that...

Answer 11

as of now, no but ill try to go over and see

can you help me with this last one

(x^4 + x)^3 (x^2 - 1)^2

find the derivative pls

Answer 12

overall... product rule... with chain rule inside

Answer 13

ofcourse but ask that as a "new" question

Answer 14

agreed