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Find the integral on ln(x).

Integrate by parts, identifying that dv/dx = 1, u = ln(x) and therefore v = x and du/dx = 1/x. Sub into the parts equation to find the answer to be xln(x) - x + c.
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Answered by Daniel O. • Maths tutor
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Sine Rule

The sine rule is a very powerful tool used in mathematics to calculate unknown sides and angles of triangles when we only know some of the information. For example if we have a triangle and we know two angle...
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Answered by Hugo G. • Maths tutor
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I'm supposed to calculate the differential of f(x)= sin(x)*ln(x)*(x-4)^2 using the product rule. I know what the product rule is but I can't split this into two bits that are easy to differentiate. How do I do it?

You say you are familiar with the product rule i.e. f(x)=u(x)v(x) f'(x)= u(x)v'(x)+v(x)u'(x) (Equation 1) OK so why don't we try applying that here let's try splitting the function in this problem down into ...
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Answered by William H. • Maths tutor
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How do you form a Cartesian equation from two parametric equations?

If the two parametric equations have the form x = a t + b and y = c t + d then the first step is to rearrange one to make the parameter 't' the subject. We then substitute this equation for 't' into the othe...
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Answered by Alexander L. • Maths tutor
18988 Views

The curve C has the equation (x^2)+4xy-8(y^2)+27=0. Find dy/dx in terms of x and y.

dy/dx= (x+2y)/(8y-2x)
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Answered by Emily O. • Maths tutor
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