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Find the derivative of the following function with respect to x. y = 5e^x−2xsin(x)

So, what I would be looking for from students who are answering this questions are the application of differentiation techniques that they would have been taught at Year 12. The first step in answering this ...
NH
Answered by Niall H. • Maths tutor
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Given y = 9x + 1/x, find the values of x such that dy/dx=0

We are given y as a function of x, let's first compute dy/dx, and then solve the equation dy/dx =0. dy/dx = 9 -1/x 2 . Then dy/dx = 0 is equivalent to 9 = 1/x 2 . Taking x 2 on the LHS and 9 on the RHS we ob...
MP
Answered by Martin P. • Maths tutor
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Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.

QUOTIENT RULE: [u(x) / v(x)]' = [u'(x)v(x) - u(x)v'(x)] / v 2 We have: u(x) = x 4 - 1, hence u'(x) = 4x 3 v(x) = x 4 + 1, hence v'(x) = 4x 3 So we have: [(4x 3 ) (x 4 + 1) - (4x 3 ) (x 4 - 1)] / (x 4 + 1) 2 ...
TA
Answered by Thomas A. • Maths tutor
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Find dy/dx, given that y=(3x+1)/(2x+1)

Since the equation for y is given in the format y=u/v, the use of the quotient rule is the easiest way to find the differential of this equation. The quotient rule states, (vu'-uv')/v^2 is equal to the diffe...
Answered by • Maths tutor
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Imagine a sector of a circle called AOB. With center O and radius rcm. The angle AOB is R in radians. The area of the sector is 11cm². Given the perimeter of the sector is 4 time the length of the arc AB. Find r.

11 = 1/2 r 2 RAB = x = rRr + r + x = 4x2r = 3rRR = 2/3r²R = 22r² = 33r = √33
AS
Answered by Alice S. • Maths tutor
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