Find-dy-dx-x-2-3-6-x-1-3-to-it-simplest-form-

Question Number 28280 by Cheyboy last updated on 23/Jan/18

F i n d d y / d x

x^{\frac{2}{3}} {(6 - x)}^{\frac{1}{3}} t o i t s i m p l e s t f o r m

Commented by abdo imad last updated on 23/Jan/18

w e h a v e y (x) = {(x^{2} (6 - x))}^{\frac{1}{3}} = {(- x^{3} + 6 x^{2})}^{\frac{1}{3}} s o

\frac{d y}{d x} (x) = \frac{1}{3} {(- 3 x^{2} + 12 x)}^{- \frac{2}{3}} .

Commented by Cheyboy last updated on 23/Jan/18

s i r d b o o k i s h a v i n g d i f f e r e n t t h i n g

Commented by abdo imad last updated on 23/Jan/18

t r u s t y o u r s e l f s i r b e c a u s e a l o t s o f b o o k s a r e f u l l w i t h e r r o r

a n d p e r h a p s t h e b o o k h a v e g i v e n a n o t h e r f o r m o f d e r i v a t i v e

e q u a l t o t h i s m y a n s w e r i s c o r r e c t \dots

Commented by Cheyboy last updated on 24/Jan/18

o k t h a n k z s i r

Answered by ajfour last updated on 24/Jan/18

y = x^{2 / 3} {(6 - x)}^{1 / 3}

\ln y = \frac{2}{3} \ln x + \frac{1}{3} \ln (6 - x)

\frac{1}{y} \frac{d y}{d x} = \frac{2}{3 x} - \frac{1}{3 (6 - x)}

\frac{d y}{d x} = y [\frac{12 - 2 x - x}{3 x (6 - x)}]

\frac{d y}{d x} = \frac{x^{2 / 3} {(6 - x)}^{1 / 3} (4 - x)}{x (6 - x)}

= \frac{4 - x}{x^{1 / 3} {(6 - x)}^{2 / 3}} .

Commented by Cheyboy last updated on 24/Jan/18

E x a c t l y t h a t z w h a t z i n t h e b o o k

Commented by Cheyboy last updated on 24/Jan/18

G o d b l e s s u s i r

Commented by abdo imad last updated on 24/Jan/18

f o r t h i s d e r i v a t i v e n o n e e d t o u s e l n . .