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Give the first and second derivative of the function f(x) = 5/x - 9x + 4

Re-write f(x) as f(x) = 5x^(-1) - 9x + 42) Find first derivative as usual - multiply each term by it's power and subtract 1 from the power:f'(x) = (-1)(5x^(-2)) - (1)(9)Simplify to get f'(x) = -5/x^(2) - 9Fi...
HB
Answered by Harvey B. • Maths tutor
3336 Views

Via the product rule, or otherwise, differentiate 'y = xsin(x)'.

SInce, for y = uv, dy/dx = uv' + vu', where u' = du/dx, therefore:dy/dx = (1 sin(x)) + (x cos(x)) = sin(x) + xcos(x)
HM
Answered by Howard M. • Maths tutor
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Show that sqrt(27) + sqrt(192) = a*sqrt(b), where a and b are prime numbers to be determined

We want to get the the sqrt(27) and sqrt(192) so that they have the same number in the square so they can then be added together. We will look at the factorisation of 27, 192. We can see 27 is divisible by 3...
LH
Answered by Luke H. • Maths tutor
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What is the integral of ln x dx

as ln x is not a standard integral given in the formula booklet, but it’s derivative is a standard derivative, you can split ln x into 1 times ln x. This allows you to use the integral product rule method wh...
AL
Answered by Alex L. • Maths tutor
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Find the roots of x^3 + 4x^2 - 5x

X=0,-5,1
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Answered by Jack W. • Maths tutor
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