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Find dy/dx from the equation 2xy + 3x^2 = 4y

Firstly we must notice that we can differentiate each term separately. Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and v=y and u...
MM
Answered by Murray M. • Maths tutor
5009 Views

Find the set of values for which x^2 - 7x - 18 >0

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -2. ...
CW
Answered by Charlotte W. • Maths tutor
17287 Views

Differentiate y = √(1 + 3x²) with respect to x

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In th...
WT
Answered by Walter T. • Maths tutor
9016 Views

Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If yo...
JB
Answered by Jessica B. • Maths tutor
19992 Views

How do you do simple integration?

If you have an expression like 6x^2, to integrate it you have to add 1 to the power. Therefore, the new power will be 3. Then divide the whole expression by the new power so it will be 6x^3 divided by 3, whi...
DS
Answered by Della S. • Maths tutor
3706 Views