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A and B have coordinates (2,3) and (5,15), respectively. Together they form line l. Find the equation for the line r that goes through C(7,-2) and is perpendicular to l. Give the answer in the format of y=mx+b

To get the equation that describes l, we'll need to get the slope first: (15-3)/(5-2)=12/3=4r is perpendicular to l so it's slope is given by: -1/4To get b we calculate: -2=7*(-0.25) + b <=> b = -1/4r:...
TD
Answered by Tutor376397 D. • Maths tutor
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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
3539 Views

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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