Math question, plz help?

Question

find the derivative of sqrt (5x+12)

Answer 1

sqrt(5x + 12)
= (5x + 12)^(1/2)

d/dx [(5x + 12)^(1/2)]
Power rule, then chain rule:
= (1/2)(5x + 12)^(-1/2) * d/dx[5x + 12]
= (1/2)(5x + 12)^(-1/2) * 5
= 5 / [2(5x + 12)^(1/2)]

Answer 2

To find the derivative of sqrt(5x + 12) we'll need to use the chain rule.

The inside term is 5x + 12.
The outside term is sqrt(5x + 12) which I'll simplify to
(5x+12) ^ 1/2

So to derive the inside, 5x + 12 simply becomes 5

The outside term is using the power rule, so we take the 1/2 from the sqrt and put it out front, like so:

(5)(1/2)

Then we subtract one from the power [1/2 becomes -1/2], and
we're done [the term becomes [5x + 12] ^-1/2 from the power rule]:

(5) from inner portion
(1/2)(5x+12)^-1/2 from the outer portion

(5)(1/2)(5x+12)^-1/2 or

5/(2*sqrt(5x+12)) as a more appropriate final answer.

Hope this helps :)

Answer 3

You can rewrite sqrt (5x+12) as (5x + 12)^1/2

Now say y = 5x+12. Using that relationship, you rewrite the formula to say:

(y^1/2)(dy/dx)(dx) (the brackets here representing multiplication)

Differentiating y^1/2 gives (1/2)y^-1/2.

Dy/dx = 5

Substituate it all in and you get:

{(1/2)y^-1/2}{5} dx = (5/2)y^-1/2

Now substitute x back in and you get the final answer:

(5/2)(5x+12)^-1/2

Hope that helps

Answer 4

y=sqrt (5x+12)

y'= 5/(2 sqrt (5x+12))

Answer 5

let sqrt(5x + 12) =y
squaring on both sides
5x + 12 = y^2
y^2 = 5x + 12
differentiating with respect to x
2 y(dy/dx) = 5(1) + 0
2y(dy/dx) = 5
dy/dx = 5/2y
=5/(2(sqrt(5x + 12))
=(5/2)*[(5x + 12)^(-1/2)]

Answer 6

d (5x + 12) ^ ½ / dx
  = ½ (5x +12) ^ (-½) d(5x +12) / dx
  = 5 / [ 2 (5x + 12) ^ ½ ]