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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
3193 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
12600 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
3522 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
3463 Views

Differentiate 5x^3 + 4x^2 + 5x + 9

Differentiate 5x 3 + 4x 2 + 5x + 9The rules from polynomial differentiation: d(ax n ) / dx= a(nx n-1 ) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules in conjunction we get : 5(3x 3-1 ) + 4(2x...
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Answered by Annabelle S. • Maths tutor
4137 Views