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Find minimum and maximum of x^2+1 if they exist

There are several methods of finding the extrema(plural of extremums or in other words minimum or maximum values) of a function. For now we will analyse the function using the dy/dx of f(x)=y=x 2 +1, f ` (x)...
PG
Answered by Pavel G. • Maths tutor
5211 Views

Differentiate xcos(x) with respect to x

We have two functions multiplied together: x and cos(x). Therefore we have to use the product rule. First differentiate x and leave cos(x) untouched, so we get 1(cos(x))=cos(x). Then differentiate cos(x) and...
IL
Answered by Ioannis L. • Maths tutor
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What is the integral of x sin(x) dx?

Find the following integral: ∫ x sin(x) dx This question is a good candidate for the integration by parts method, as it is the product of two different 'parts'. Step 1) Recall that if you have an integral of...
SF
Answered by Shaun F. • Maths tutor
348518 Views

Solve the simultaneous equations: x^2+y^2=36 ; x=2y+6

Substitute x in terms of y into the first equation: (2y+6) 2 +y 2 =36 Use FOIL to expand the brackets 4y 2 +24y+36+y 2 =36 => 5y 2 +24y=0 y(5y+24)=0 => y=0 or y=(-24)/5 Substitute these values of y int...
DB
Answered by Daniel B. • Maths tutor
33681 Views

Find the derivative of f(x)=x^2log(2x)

Use the product rule (f'(x)=u'v+uv') Let u=x 2 => u'=2x Let v=log(2x) => v'=2/(2x) => v'=1/x Therefore f'(x)=2xlog(2x)+x 2 /x f'(x)=2xlog(2x)+x
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Answered by Daniel B. • Maths tutor
9945 Views