AboutAlon Mandes Expertise Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems.
Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience 1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Question what are the derivatives of these functions a)h(x)=xtan(2*underrootx)+7, b)k(x)=x^2sec(1/x),c)r=sin@^2cos2@
Answer Let's start with the 1st function :
H(x)=7+x*tan[2*sqrt(x)]
H'(x)=0+1*tan[2*sqrt(x)]+x*2*[1/2sqrt(x)]*[1/cos^2(2*sqrt(x))]
Explanation :
1. [f(x)*g(x)]'=f'(x)*g(x)+f(x)*g'(x)
2. tan[f(x)]'=f'(x)*1/cos^2(f(x)) & in our case f(x)=2*sqrt(x).
So, H'(x) becomes : tan[2sqrt(x)] + sqrt(x)/cos^2(2sqrt(x)).
The 2nd function :
K(x)=(x^2)*sec(1/x)
K'(x)=(x^2)'*sec(1/x)+(x^2)*sec(1/x)' "as in 1 above"
K'(x)=2x*sec(1/x)+(x^2)*(-1/x^2)*sec(1/x)tan(1/x)
K'(x)=sec(1/x)[2x-tan(1/x)]
Explanation :
1.sec(x)'=sec(x)tan(x)
2.sec(1/x)'=(1/x)'*sec(1/x)tan(1/x)
The 3rd function :
r(Ø)=sin(Ø^2)cos(2Ø)
r'(Ø)=[sin(Ø^2)']cos(2Ø)+sin(Ø^2)*[cos(2Ø)]'
r'(Ø)=[2Ø*cos(2Ø)]cos(2Ø)+sin(Ø^2)*[-2sin(2Ø)]
r'(Ø)=2Ø*cos^2(Ø)-2*sin(Ø^2)sin(2Ø)
Explanation:
1.cos(ax)'=-a*sin(x)
2.cos(x^2)=-2x*sin(x^2)
Note : if you meant r(Ø)=sin^2(Ø)cos(2Ø) , I will leave it to you
as an exercise.
