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Find dy/dx for f(x)=3x^2 +5x

This is a simple differentiation example of a polynomial, where one uses the the standard algorithm - i.e.[nx^n-1] Ina polynomial, one differentiates all parts separately. First Take 3x^2. Multiply by the po...
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Answered by Merin R. • Maths tutor
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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
6404 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
4097 Views