Question

find dx/dt by implicit differentiation: x-sqrt(t) = tx
PLEASE HELP ME! AND EXPLAIN Step bY Step sO I CAN UNDERSTAND! THANK YOU!

Answer 1

basically you need to find x'

Answer 2

t is the variable you differentiating with respect to

Answer 3

x-sqrt(t) = tx

differentiate both sides

Answer 4

d/dt [x-sqrt(t)] = d/dt [tx]

Answer 5

x' - 1/2sqrt(t) = d/dt [tx]

Answer 6

right hand side you must use 'product rule'

Answer 7

can you take this from here ?

Answer 8

after i take the product rule on the right side, then is that it?

Answer 9

wat do you get after taking product rule ?

Answer 10

you need to solve for x' in the end, and then thats it :)

Answer 11

so it would be d/dt (t)'x + (t)(x)' right?

Answer 12

what would be the derivative of t???

Answer 13

derivative of 't' with respect to 't' is 1

d
-- (t) = 1
dt

Answer 14

just like x?

Answer 15

so my right side answer would be just x+t?

Answer 16

yes ! derivative of 'x' with respect to 'x' is 1

Answer 17

not exactly,

derivative of 'x' with respect to 't' is NOT 1

Answer 18

let me show the complete solution

Answer 19

x-sqrt(t) = tx

differentiate both sides with respect to t

d/dt[x-sqrt(t)] = d/dt[tx]

x' - 1/2sqrt(t) = d/dt [tx]

x' - 1/2sqrt(t) = tx' + x

solve for x' now

Answer 20

x' - 1/2sqrt(t) = tx' + x

x'(1-t) = x + 1/2sqrt(t)


x + 1/2sqrt(t)
x' = ------------
1-t

Answer 21

you may simplify if you want, else you can leave it as it as

Answer 22

btw, x' is the dx/dt

Answer 23

Thank you so much!

Answer 24

np :)