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Find the equation of the normal of the curve xy-x^2+xlog(y)=4 at the point (2,1) in the form ax+by+c=0

differentiating: xy'+y-2x+(x/y)y'+log(y)=0rearranging: y'=y(2x-y-log(y))/x(1+y)at (2,1): y'=3/4 so gradient of normal at (2,1) is -4/3so the equation of the normal is y-1=(-4/3)(x-2)which is equivalent to...

Answered by Sam L. • Maths tutor

2652 Views

Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2

First express as a single logarithm as follows. The number in front of the logarithm remembering log rules can be rewritten as the power of the number in the bracketsSo rewriting the LHS
log₃

Answered by Theranjit S. • Maths tutor

6974 Views

differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we w...

Answered by Elizabeth W. • Maths tutor

2214 Views

integrate from 0 to 2: 2x*sqrt(x+2) dx

There are a few ways to go about this question. I will do a substitution using u=(x+2)^1/2. From this equation we need to find x in terms of u, the new limits of the integral and dx in terms of ...

Answered by Tom W. • Maths tutor

9642 Views

How do you differentiate using the chain rule?

At first the chain rule can seem quite daunting and convoluted but with a few examples over the course of this lesson, it will seem simpler and more intuitive.
The chain rule is used where the equat...

Answered by Alex K. • Maths tutor

2540 Views