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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

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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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Q4 on 2017 Edexcel C4 paper, concerns differentiation of multiple variables.

(a) Asks to differentiate an equation C: 4x² - y³ - 4xy + 2^y = 0Then use the fact that point P (-2,4), lies on C to find an expression for dy/dx Differential of form 8x - ...

Answered by Alexander W. • Maths tutor

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