help - dy/dx

[gleaming comet]

can some1 explain the steps

[crystal anchor]

root x can be written as 1/2

dydx 3root x + 1 = dy/dx 3x^1/2 + 1 = 3/2 x^-1/2

so our gradient

is 3/2 x^-1/2

5x - 10y + 7 = 0

10 y = 5x + 7

y = 1/2x + 7/10

perpendicular gradient to this is -2

[crystal anchor]

= 3/(2 root x)

oh and to find the normal

we do 1/3/(2rootx)

which simplifies to

.- (2 root x / 3)

now - (2root x / 3) = -2x

when u solve it

u should get

x = 9

now to find the y coordinate

slot it into the curve equation

3 root 9 + 1 = 3x3 + 1 = 10

(9, 10)

so the gradient is -2 x

and the point is (9, 10)

y = -2x + c

10 = -18 + c

y = -2x + 28