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Differentiate 5x^2+5y^2-6xy=13 to find dy/dx

This is an example of implicit differentiation, where the function in question involves two variables (x and y) and it is hard to rearrange to create a neat "y=..." equation. To differentiate this ...
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Answered by Henry S. • Maths tutor
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Find Dy/Dx of (x^2+4x)^3

So here we need to use the chain rule in order to differentiate the equation. To start you take the function inside the bracket x 2 +4x and differentiate it to Du/Dx= 2x + 4 this is known as u. do the you di...
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Answered by Sam O. • Maths tutor
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Show that the equation 2sin^2(x) + 3sin(x) = 2cos(2x) + 3 can be written as 6sin^2(x)+3sin(x) - 5 = 0. Hence solve for 0 < x < 360 degrees. Giving your answers to 1.d.p.

2sin^2(x) + 3sin(x) = 2cos(2x) + 32sin^2(x) + 3sin(x) = 2(cos^2(x) - sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2(1- 2sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2 - 4sin^2(x) + 36sin^2(x) + 3sin(x) - 5 = 0 let sin(x) = yT...
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Answered by Tom A. • Maths tutor
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The curve C has equation y = (x^2 -4x - 2)^2. Point P lies on C and has coordinates (3,N). Find: a) the value of N. b) the equation of the tangent to C at the point P, in the form y=mx+c where m and c are constants to be found. c) determine d^2y/dx^2.

a) Sub x=3 into the given equation. N is found to be 25.b) Finding dy/dx gives me, as the first differential is the gradient.First differentiate the power and then multiply the differential of the expression...
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Answered by Tom A. • Maths tutor
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Two masses A and B, 2kg and 4kg respectively, are connected by a light inextensible string and passed over a smooth pulley. The system is held at rest, then released. Find the acceleration of the system and hence, find the tension in the string.

First we draw a diagram of this system (on whiteboard). Remember to label diagram correctly - the tension on both sides act towards each other. Since B is a larger mass, we know that mass A will move upwards...
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