# Sum Rule

The Sum Rule, a fundamental concept in probability theory, governs the calculation of probabilities for mutually exclusive events. In essence, it states that the probability of the union of two or more exclusive events is the sum of their individual probabilities. This rule provides a concise and powerful tool for analyzing and predicting outcomes in various fields, from statistics and finance to machine learning. By understanding the Sum Rule, one gains a foundational grasp of probability principles essential for making informed decisions and modeling uncertainties in diverse scenarios.

Questions

- What is the derivative of #f(x) = xlnx-lnx^x#?
- How do you differentiate #f(x)=1/x+x# using the sum rule?
- How do you differentiate #f(x)=x/(x-1)^2+x^2-4/(1-1x)# using the sum rule?
- How do you differentiate #f(x)=x/(x-1)^2+x^2-4/(1-2x)# using the sum rule?
- Can you saolve this please? thanks! #y''-2y'+y=e^x/sqrt(4-x^2)#
- Let #A# be the area of a circle with radius #r#. If #(dr)/(dt)=2#, what is #(dA)/(dt)# when #r=1#?
- How do you find the derivative of #y = f(x) - g(x)#?
- What is #sum_(k=1) ^n# #(3k+1)#?
- How do you differentiate #f(x)=(x-3)^2+(x-4)^3# using the sum rule?
- How do you differentiate #f(x)=sinx+cosx-x^3# using the sum rule?
- How do you differentiate #f(x)=1/x+1/x^3# using the sum rule?
- How do you differentiate #f(x)=3/x-5/(1-x)# using the sum rule?
- How do you differentiate #f(x)=x+x-2x# using the sum rule?
- How do you differentiate #f(x)=sinx-1/(xcosx)# using the sum rule?
- How do you differentiate #f(x)=4x^5-5x^4# using the sum rule?
- How to find formula for the nth derivative of #f(x)=cos(ax+b)#?
- How do you differentiate #f(x)=(x-5)^3-x^2+5x# using the sum rule?
- How do you differentiate #f(x)=7x^3-x^2+x# using the sum rule?
- How shall I proceed in this sum? If #x=sint# and #y=sin2t#, prove that (i) #(1-x^2)(dy/dx)^2=4(1-y^2)# (ii) #(1-x^2)(d^2(y)/dx^2)-xdy/dx+4y=0#
- How do you find the derivative of #y=f(x)+g(x)#?