Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?

The key concepts to apply in this question will be the product and chain rules, namely: if  f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x).

Equivalently, you may prefer to apply the quotient rule and the chain rule.

To answer this question, you also need to know that x is a stationary point if f'(x)=0.

Worked solution:

Here we have g(x)=sin(x) and h(x)=(x2+1)-1. We differentiate these to get g'(x)=cos(x) and h'(x)=(-1)(2x)(x2+1)-2, using the chain rule to differentiate h(x).

Now we put these together (using the product rule) to get f'(x)=sin(x)(-1)(2x)(x2+1)-2+cos(x)(x2+1)-1.

Finally, the question asks for the final answer in the form of a single fraction, so we rearrange to get: f'(x)=(cos(x)*(x2+1) - (2x)*sin(x))/(x2+1)2.

To finish off we need to check the value of f'(x) at =0: f'(0)=1/12=1. This is not 0, so x=0 is not a stationary point.

BC
Answered by Bromlyn C. Maths tutor

4844 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the gradient of the line Y = X^3 + X + 6 when X = 4


Let f(x)=x^3 - 2x^2 + 5. For which value(s) of x does f(x)=5?


Shower-cleaner liquid is sold in spray bottles. The volume of liquid in a bottle may be modelled by a normal distribution with mean 955 ml and a standard deviation of 5 ml. Determine the probability that the volume in a particular bottle is:


Express 2 ln(3) + ln(11) as a single natural logarithm


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences