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Differentiating equations of the type ln[f(x)]

To solve such equations we take advantage of log lawes to simplify the problem . E.g ln[sqrt(1-x 2 )] = ln[(1-x 2 ) 1/2 ] = 1/2ln[1-x 2 ] After simplifing the problem we can differentiate with respect to x y...
MS
Answered by Mousa S. • Maths tutor
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How do I integrate x/(x^2 + 3) ?

To solve this you need to integrate by substitution. You can spot this because the differential of the bottom of the fraction is a multiple of the top part, showing this quickly; if u = x 2 + 3 (the bottom p...
KM
Answered by Knox M. • Maths tutor
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integrate by parts the equation dy/dx = (3x-4)(2x^2+5).

The equation we use to integrate by parts is y = uv - ∫ v(du/dx) dx + c so we separate dy/dx into u=(3x-4) and dv/dx=(2x 2 +5) however we still need to find du/dx and v, by differentiating u (bring the power...
AH
Answered by Abby H. • Maths tutor
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A curve is defined by the parametric equations x=t^2/2 +1 and y=4/t -1. Find the gradient of the curve at t=2 and an equation for the curve in terms of just x and y.

To find the gradient of the curve at t=2 we need to find an expression for dy/dx and then substitute in for t=2. We can make use of the chain rule to find this expression because dy/dx = (dy/dt)/(dx/dt) and ...
SC
Answered by Steven C. • Maths tutor
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Integrate x*ln(x) with respect to x

First identify that integration by parts is required. Then seperate the integration so u = ln(x) dv/dx = x then, du/dx = 1/x v = (1/2)x^2 . And using the integration by parts formula with these substitutions...
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Answered by Ana S. • Maths tutor
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