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When do I use the product rule as opposed to the chain rule?

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x 2 * x+1 or more complex functions like sinxcosx. The chain rule is use...
LU
Answered by Lota U. • Maths tutor
4361 Views

Let f (x) = sin(x-1) , 0 ≤ x ≤ 2 π + 1 , Find the volume of the solid formed when the region bounded by y =ƒ( x) , and the lines x = 0 , y = 0 and y = 1 is rotated by 2π about the y-axis.

Draw a rough sketch of the graph of f(x) = sin(x-1) to get an idea of what the region looks like. Realise that the normal volume of revolution for the area between x axis and the f(x) is given by V = pi* int...
AS
Answered by Ankur S. • Maths tutor
7505 Views

Solve these simultaneous equations. x^2+y^2=9, x-y+3=0

Rearrage so you have x+3=y, and x 2 +y 2 =9. Substitute the equation into another so you have x 2 +(x+3) 2 =9. Expand the brackets so that you have x 2 +x 2 +6x+9=9. Then you rearrange so it's all on one sid...
AB
Answered by Adam B. • Maths tutor
6786 Views

A line runs between point A(5,9) and B(11,1). Find the equation of the line. Point C lies on the line between A and B. The line with equation 2y=3x+12 also crosses through point C. Find the x coordinate of Point C.

For the first part it would be a good idea to sketch out the graph. Then using the formula 'change in y/change in x' find the gradient of the line (-4/3). You can then either use the formula y=mx+c and put i...
AT
Answered by Amelia T. • Maths tutor
3334 Views

How do I find out where two functions meet on a graph?

Both equations should be given with variables of y and x. They may however not be given in the form y=mx+c where m and c are constants, the equation could be given in the form of a circle (y-a) 2 +(x-b) 2 =r...
TR
Answered by Thomas R. • Maths tutor
3821 Views