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Given that y = (sin(6x))(sec(2x) ), find dy/dx

We can find dy/dx by using the product rule: If y=uv then dy/dx = u (dv/dx)+ v (du/dx). In this question u= sin(6x) and v= sec(2x).So du/dx= 6cos(6x) and dv/dx=2sec(2x)tan(2x), using our rules for differenti...
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Answered by Eli H. • Maths tutor
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a) Differentiate and b) integrate f(x)=xcos(2x) with respect to x

To differentiate xcos(2x), you first have to use the product rule, because this function is two functions (x and cos(2x) multiplied togetherNow you have x*(cos(2x))'+cos(2x)To differentiate cos(2x) you have ...
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Answered by Danila M. • Maths tutor
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Find 1 + (1 + (1 + (1 + (1 + ...)^-1)^-1)^-1)^-1

1 + (1 + (1 + (1 + (1 + ...) -1 ) -1 ) -1 ) -1 This pattern goes infinitely. The first step to this question, is to observe. Observe the pattern. Look at the brackets. Do you see how it repeats itself? Let's...
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Answered by Jason Y. • Maths tutor
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5 White Socks and 3 Black socks are in a drawer. I take out two socks. What is the probability the socks are the same colour?

Problem Tackles: Counting Probabilities, Non-replacement probability problems. Keeping track of events Total number of socks: 5 + 3 = 8Scenarios: Could pick two white socks or two black socksP(Picking two wh...
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Answered by Bonnor S. • Maths tutor
7320 Views

Find a solution for the differential equation dy/dx=exp(-y)*sin2x which passes through the origin.

First separate the variables so that the left side of the equation is an expression only in terms of y and the right side only in terms of x.exp(y)dy=sin2x dxSecondly both sides have to be integrated to obta...
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Answered by Felix B. • Maths tutor
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