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How would you differentiate f(x) = 2x(3x - 1)^2 using the chain rule?

In order to differentiate this expression, you need to use the chain rule. The chain rule gives: f'(x) = uv' + u'v. The u and the v are two parts of the original function f(x). The apostrophe ' at the end me...
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Answered by Sam E. • Maths tutor
16247 Views

Find the derivative of f where f(x)=a^x.

This is a difficult question that you only need to know the result of.However, it's a good exercise to derive it. Starting with f(x)=a x we can take the natural logarithm of both sides (so we can use one of ...
LR
Answered by Larry R. • Maths tutor
4893 Views

How would you express (11+x-x^2)/[(x+1)(x-2)^2] in terms of partial fractions?

The first thing to consider when converting an expression to impartial fractions is how many fractions you will have in the end. With linear (no powers) brackets, found in the denominator of your initial fra...
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Answered by Matthew M. • Maths tutor
7993 Views

f(x) = (4x + 1)/(x - 2). Find f'(x)

Quotient rule: (vu' - uv')/v^2 u = 4x + 1 u' = 4 v = x - 2 v' = 1 Input into formula: [(x - 2)(4) - (4x + 1)(1)](x - 2)^2 Simplify: [4x - 8 -4x - 1]/(x - 2)^2 = -9/(x - 2)^2
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Answered by Salah S. • Maths tutor
13778 Views

How do I differentiate something in the form f(x)/g(x)?

To differentiate the quotient of two functions f(x)/g(x) you can use the quotient rule, the formula of which is: (f'(x)*g(x)-f(x)*g'(x))/g 2 (x) it is important to remember which part you have to differentia...
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Answered by Riccardo P. • Maths tutor
9921 Views