Given that x=ln(t) and y=4t^3,a) find an expression for dy/dx, b)and the value of t when d2y/dx2 =0.48. Give your answer to 2 decimal place.
a) Firstly, differentiate x and y with respect to t.
Giving you dx/dt = 1/t and dy/dt = 12t2
dy/dx is found using the chain rule:
dy/dx = dy/dt x dt/dx = 12t3
b) You will need to differentiate dy/dx again with respect to t, to do this:
d2y/dx2=36t2 x dt/dx = 36t3
36t3=0.48
t=(0.48/36)1/3
t=0.24
SW
Related Maths A Level answers
All answers ▸Let f(x) = 5x^4 + 6x^3 + 3, find dy/dx at x = 3
A curve has the equation y=12+3x^4. Find dy/dx.
a) Solve the following equation by completing the square: x^(2)+ 6x + 1= 0. b) Solve the following equation by factorisation: x^(2) - 4x - 5 = 0 c) Solve the following quadratic inequality: x^(2) - 4x - 5 < 0 (hint use your answer to part b)
Solve the following equation, give the answer/answers as coordinates. y=3x^2 , y=2x+5.