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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
7226 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
5416 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
6281 Views

A curve has parametric equations x=2t, y=t^2. Find the Cartesian equation of the curve.

x=2t --> t= x/2 y=t 2 = (x/2) 2 . So the Cartesian equation is y=x 2 /4.
KW
Answered by Katarzyna W. • Maths tutor
15810 Views