Calculus
posted by Anonymous .
If x = t^2 + 1 and y = t^3, then d^2y/dx^2 =
I know I can solve for t in terms of x and substitute that into y = t^3 and find the double derivative.
I also know that I can take the derivative of x and y then divide dy/dt by dx/dt. Then take the derivative to get the answer.
However, my question is why can't you find d^2x/dt^2 and d^2y/dt^2 and divide to find d^2y/dx^2?
Like
x = t^2 + 1
dx/dt = 2t(dt/dt) + 0(dt/dt)
d^2x/dt^2 = 2(dt/dt) = 2
y = t^3
dy/dt = 3t^2(dt/dt)
d^2y/dt^2 = 6t(dt/dt)
d^2y/dx^2 = (d^2y/dt^2)/(d^2x/dt^2)
d^2y/dx^2 = 6t / 2 = 3t
The correct answer, however, is 3/4t. Why? Am I doing something wrong .?
 Calculus  bobpursley

Calculus 
Anonymous
Ah, I see. Just for confirmation, d^2x != dx^2, correct?
Respond to this Question
Similar Questions

Math
Find the Maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. 28 inches Well, finally a calculus problem. Ok, we know that the area for a rectangle is A=l*w and the perimeter is P=2(l+w) … 
ALGEBRA 1!PLZ HELP!
Use the Substitution method to solve the system of equations. y  2x = 5 3y  x = 5 Solve the first equation for y. y = 2x5 Substitute that for y in the second equation and solve for x. Then use the value of x to substitute back … 
algebra
use substitution to solve the linear system 3xy=15 x+2y=2 Solve for y in one formula, and then substitute that value for y in the other formula to solve for x. Once you find x, substitute that value into either formula to get the … 
algebra
use substitution to solve the linear system 3x+2y=5 4x3y=16 help plz!!! Solve for y in one formula, and then substitute that value for y in the other formula to solve for x. Once you find x, substitute that value into either formula … 
algebra
5x2y=5 y5x=3 substitution Substitute 5x +3 for y in the first equation, then solve it for x. Substitute 5x +3 for y in the first equation, then solve it for x. When I subsitute 5x+3 into the equation I get x=1/5 and y=2 is this … 
Calculus
How do I use the product rule to solve these two questions. Much appreciated! xo Find the derivative for k(x) = (5x4 + 2)(3sin x) Find the derivative for m(x) = ex cos x at x = 1 
Math  Derivative of a polynomial function(check)
The red squirrel population, p, in a neighborhood park can be modelled by the function p(t)= srqt(210t+44t^2), where t is time in year. a) Determine the rate of growth of the squirrel population at t= 2years Ans: find the 1st derivative … 
Calculus
y= ln3x *e^2x^2 + sin5x^2 find the derivative. i know what to do. but what is the derivative of ln3x? 
calculus
Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results … 
Chemistry
4.00 mol of solid A was placed in a sealed 1.00L container and allowed to decompose into gaseous B and C. The concentration of B steadily increased until it reached 1.20 M, where it remained constant. A(s) <> B(g)+C(g) …