Top answers

What is the first derivative of y=5z(1+2z2)? Is this a minimum, maximum or turning point?

You should not be put off by the algebraic letters used, substituting x's for z's is absolutely fine. For the first part of the question, since the equation involves the product of two terms, there are two w...
TR
Answered by Tom R. • Maths tutor
4508 Views

integrate function (x^4+3x)/(x^2) with respect to x

split the integral into (x^4)/(x^2) and (3x)/(x^2) which becomes x^2 and 3*(1/x). These can now be integrated separately and added together after the integration. first integral: raise the power form 2 to 3,...
CS
Answered by Calum S. • Maths tutor
4236 Views

Solve the simultaneous equations: y-2x-4 = 0 (1) , 4x^2 +y^2 + 20x = 0 (2)

Re-arrange (1) : y = 2x + 4 Square both sides: y^2 = 4x^2 + 16 Substitute (1) into (2) and simplify: 2x^2 + 9x + 4 = 0 Factorise the equation: (2x+1)(x+4) = 0 Solve for x: x = -1/2 and x = -4 Substitute thes...
GA
Answered by Giorgos A. • Maths tutor
10180 Views

How do we know that the derivative of x^2 is 2x?

To answer this we must remember that the derivative at a point on a curve, in this case x^2, is simply the value of the gradient of the line that just touches that point on the line. We can start by approxim...
JM
Answered by Jamie M. • Maths tutor
5047 Views

Find the integral of ln(x)

To solve this, we must use integration by parts as we can’t solve it directly. The formula for integration by parts is integral(U dV)=U V-integral(V*dU). The trick with this is to set dV=1 and to set U=ln(x)...
MR
Answered by Matilda R. • Maths tutor
6044 Views