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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 3x²* x+1 or more complex functions like sinxcosx.

Th...

Answered by Lota U. • Maths tutor

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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 pu...

Answered by Amelia T. • Maths tutor

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How do I intregrate ln(x)?

To integrate ln(x) we will have to use integration by parts.

The equation for integration by parts is: (then equation written on the whiteboard).

In the case of ln(x), let v=ln(x) ...

Answered by Isabelle P. • Maths tutor

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A cuboid has a rectangular cross section where the length of the rectangle is equal to twice its width x cm. THe volume is 81 cm^3. a) show that the total length L cm of the cuboid is given by L=12x+162/x^2

Volume=81 cm³

b=81/2x²

L=4x+4(2x)+ 4(b)

L=4(x)+4(2x)+4(81/2x²)

L=12x+ 162/x²

Answered by Bilaal T. • Maths tutor

7977 Views

How would you integrate ln x

You would use the product rule. uv'=uv- u'vdx. In this case we would allocate u= ln x and v'=1 so u'=1/x and v=x so uv=xlnx whilst u'v=x/x=1 so we would have xln(x) -1dx. Next we would get xln(x)-x +c

Answered by Callum M. • Maths tutor

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