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Finding the tangent of an equation using implicit differentiation

y²e^2x = 3y + x²1) Differentiation: Product rule, Explicity differentiation.2) Rearrangement: Collecting terms, Making dy/dx subject.

Answered by Paul J. • Maths tutor

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We are given y=(x^2)+3x-5. Find the derivative of y in terms of x.

From the question we have, y=x²+3x-5
The rule of differentiation, is that you take the power on the x and bring it to the front, leaving the power-1 behind. In other words if you have x

Answered by Maya B. • Maths tutor

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Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt Integrate both sides: ln[2/(1+2x)] = -8e^(-2t) + c input x = 1/2, t = 0: ln(2/2) = -8*(1) + c ln 1 = 0, so c = 8ln[2/1+2x] = 8[1-e^(-2t)]

Answered by Henry F. • Maths tutor

2834 Views

Solve: 2 sin(2x) = (1-sin(x))cos(x) for 0<x<2*Pi and give any values of x, if any, where the equation is not valid

Double angle formula:Sin(2x) = 2sin(x)*cos(x)==> 2sin(x)*cos(x) = (1-sin(x))*cos(x) (2sin(x)-1+sin(x))*cos(x) = 0(3sin(x) - 1)*cos(x) = 0 i) cos(x) = 0, ii) 3sin(x) = 1 ==> sin(x) = 1/3 ...

Answered by Henry F. • Maths tutor

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How do I find the maxima and minima of f(x) = e^(x^2)?

When dealing with maxima and minima points, there are two ways to go, one of these is to first compute the first derivative of the function, check when this function is zero, and then study its sign; the ...

Answered by Jacob A. • Maths tutor

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