Sum Rule Calculus Basic Differentiation Rules Sum Rule Key Questions How do you find the derivative of #y = f(x) - g(x)#? The derivative for #y=f(x)-g(x)# works the same way as the derivative of #y=f(x)+g(x)#. #y=f(x)-g(x) => dy/dx=f'(x)-g'(x)# The quick proof is: #y=f(x)-g(x)=f(x)+(-1)g(x)# Using the sum rule and the constant rule: #dy/dx=f'(x)+(-1)g'(x)=f'(x)-g'(x)#. How do you find the derivative of #y=f(x)+g(x)#? By Sum Rule, #y'=f'(x)+g'(x)# For example, if #y=x^3+e^x#, then #y'=(x^3)'+(e^x)'=3x^2+e^x# Questions What is the Sum Rule for derivatives? How do you find the derivative of #y=f(x)+g(x)#? How do you find the derivative of #y = f(x) - g(x)#? What is the derivative of #f(x) = xlnx-lnx^x#? How do you differentiate #f(x)=1/x+1/x^3# using the sum rule? How do you differentiate #f(x)=x+x-2x# using the sum rule? How do you differentiate #f(x)=x^2-x-x(x-1)# using the sum rule? How do you differentiate #f(x)=x^3-x^2+4x-1# using the sum rule? How do you differentiate #f(x)=sinx+cosx-x^3# using the sum rule? How do you differentiate #f(x)=x+lnx^2-x^2# using the sum rule? How do you differentiate #f(x)=1/sinx-secx+tanx# using the sum rule? How do you differentiate #f(x)=1/x+x# using the sum rule? How do you differentiate #f(x)=1/x^3-x^4+sinx# using the sum rule? How do you differentiate #f(x)=4x^5-5x^4# using the sum rule? How do you differentiate #f(x)=(x-3)^2+(x-4)^3# using the sum rule? How do you differentiate #f(x)=(x-3)^2+(-x-4)^2# using the sum rule? How do you differentiate #f(x)=7x^3-x^2+x# using the sum rule? How do you differentiate #f(x)=(x-5)^3-x^2+5x# using the sum rule? How do you differentiate #f(x)=lnx^2+lnx-x# using the sum rule? How do you differentiate #f(x)=lnx+ln2x+3x# using the sum rule? How do you differentiate #f(x)=(x-2)^3+x# 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)=1/(x-1)^2+x^3-4/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? How do you differentiate #f(x)=sinx-1/(xcosx)# using the sum rule? Basic Differentiation Rules View all chapters Power Rule Chain Rule Sum Rule Product Rule Proof of the Product Rule Quotient Rule Implicit Differentiation Summary of Differentiation Rules Proof of Quotient Rule Prev Next
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