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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 log 3 (x 2 ) - log 3...
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Answered by Theranjit S. • Maths tutor
9329 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 will...
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Answered by Elizabeth W. • Maths tutor
3119 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 du. By rearr...
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Answered by Tom W. • Maths tutor
12502 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 equation that ...
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Answered by Alex K. • Maths tutor
3460 Views

Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4

Answer: f'(x) = 15x^2 + 12x -12 This is according to basic rules of differentiation and is a beginner level differentiation question as following:If f(x) = ax^nThen f'(x) = x(nx^n-1)
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Answered by Holly K. • Maths tutor
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