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y(x) = x^2(1-x)e^-2x , find y'(x) in the form of g(x)e^-2x where g(x) is a cubic function to be found

For this question, I would first expand the brackets in the given y(x) to form , x^2e^-2x -x^3e^-2x . With this form, I would then differeniate using the chain rule to then obtain the expression that can eas...
AB
Answered by Arjun B. • Maths tutor
3991 Views

When dealing with trigonometric functions such as sin, cos or tan, how do you solve the trigonometric equation when the argument of the function(s) is nx, where n is a real number not equal to 1.

In order to solve Trigonometric equations like these, you must consider how the argument of the function changes the period of the graph. There are many methods of solving equations like this, but personally...
JM
Answered by Joshua M. • Maths tutor
3643 Views

Find dy/dx when y=(3x-1)^10

We have to use the chain rule in this instance to find the differentiated value y=(3x-1)^10 suppose y=u^10 thus, dy/du = 10u^9 secondly: u=3x-1 du/dx=3 the chain rule suggests that dy/dx = du/dx *dy/du so th...
NK
Answered by Nimita K. • Maths tutor
4344 Views

If a 5 metre ladder is resting against a wall and the bottom of the ladder is 3 metres away from the wall, and someone pulls the bottom of the ladder away at a speed of 1 metre per second, calculate the speed of the top of the ladder after t seconds

After t seconds the distance between the bottom of the ladder and the wall is t metres. Let x denote the distance that the top of the ladder has moved after t seconds. Now use the theorem of Pythagoras to ob...
OB
Answered by Oliver B. • Maths tutor
3542 Views

Given y = 2x(x2 – 1)5, show that (a) dy/dx = g(x)(x2 – 1)4 where g(x) is a function to be determined. (b) Hence find the set of values of x for which dy/dx > 0

Given y = 2 x ( x 2 – 1) 5 , show that (a) d y/dx = g( x )( x 2 – 1) 4 where g( x ) is a function to be determined. dy/dx= (2)( x 2 – 1) 5 + (2x)*5(x 2 – 1) 4 (2x) dy/dx= ( x 2 – 1) 4 ( 2( x 2 – 1) + 20x 2 )...
AI
Answered by Abi I. • Maths tutor
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