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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
7329 Views

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
5480 Views

Can you explain the different valves of the heart and why they are important?

The heart consists of 4 chamber; left and right atria, plus left and right ventricles. The right atria recieves deoxygenated blood from the superior and inferior vena cava, delivering blood from the head and...
RD
Answered by Radi D. • Biology tutor
3493 Views

How would I use implicit differentiation to differentiate functions such as: y=tan^-1(ax^2+b) in the form of dy/dx=.....?

First you must write the function in terms on something you know how to differentiate, for example... by taking tan (..) of both sides the equation becomes, tan(y)= ax 2 +b. We then use implicit differentiat...
CS
Answered by Charles S. • Maths tutor
6344 Views