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Why do we have to add the +c when integrating a function

First of all it is important to know that differentiation is the opposite of integration. So if we integrate some function g(x) and get f(x), it means that when we differentiate f(x) we should get g(x). We d...
NS
Answered by Niraj S. • Maths tutor
5489 Views

Solve the following equation: 5x - 1 = 3x + 7

5x - 1 = 3x + 75x = 3x + 82x = 8x = 4
DH
Answered by Daragh H. • Maths tutor
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Show, by first principles, that the differential of x^2 is 2x.

First I would draw a Diagram of y=x 2 on the x and y plane, for x>0. Then label a generic point as (x,y), then noting that as y=x 2 we can then equate the sane point to (x, x 2 ). Then I would note that a...
KJ
Answered by Kieren J. • Maths tutor
4016 Views

Find the stationary points of the function f(x) = x^3+6x^2+2 and determine if they are local maximums or minimums.

A stationary point is defined as a point on the function where the gradient is zero, i.e f'(x) = 0 . To construct this equation we must differentiate the function, we would find f'(x) = 3x 2 +12x . The corre...
LS
Answered by Luke S. • Maths tutor
5869 Views

Calculate the derivative of x^x

This problem is best solved using implicit differentiation and by tackling each side of the equation individually. First write down the problem as "y = x^x". Recalling that log rules can be used to...
GH
Answered by George H. • Maths tutor
4278 Views