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Find the derivative of f(x)= ln(|sin(x)|). Given that f(x) has a value for all x, state why the modulus is required.

The derivative can be found by using the chain rule. i.e. let g(x) = |sin(x)|, so f(x)=ln(g(x)), hence df/dx = df/dg * dg/dx df/dg = 1/g, dg/dx = |cos(x)| so df/dx = |cos(x)|/|sin(x)| For the second part, it...
LK
Answered by Luke K. • Maths tutor
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What is implicit differentiation and how do I do it?

Implicit differentiation involves differentiating expressions for which it is difficult to rearrange into y in terms of x. It is important to note which variable is being differentiated by the other as, for ...
NO
Answered by Nicholas O. • Maths tutor
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2476 people are at a football match. The ratio of men to women is 3 : 1. How many more men than women are at the match?

Ratios are a way of comparing the amount of two things in a whole. In this case we are comparing the number of men and women in a football match, so, the total number of people at the match is equal to the s...
EB
Answered by Emma B. • Maths tutor
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Let f(x)=x^3-6x+3. i)Differentiate f(x) to find dy/dx. ii) Given that dy/dx = 12, find the value of x.

For part i) we use the basic method of differentiation by considering each term individually. The first term, x 3 goes to 3x 2 by multiplying the original term by the original power, by 3, and then subtracti...
SH
Answered by Samuel H. • Maths tutor
5350 Views

Simplify : 3a(b^2) * (a^3)b

Rearrange the terms and group: Numbers: (3*1) =3, a variables: a * (a^3) --> (1+3=4) Therefore (a^4); b variables: (b^2)*b --> (2+1=3) Therefore (b^3); Regroup: 3(a^4)(b^3)
SH
Answered by Sharleen H. • Maths tutor
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