How do you find the derivative of #18lnx+x^2+5#?

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Answer 1 · 2016-04-14T18:25:40

#18/x+2x#

Through the sum rule, to find this function's derivative, add each part's derivative to one another:

Thus, we just need to find the derivative of each part:

#d/dx(18lnx)=18d/dx(lnx)=18(1/x)=18/x#

Recall that #d/dx(lnx)=1/x#, and that #18# is just a constant being multiplied, which we can multiply by the derivative of #lnx#.

Through the power rule, we see that

#d/dx(x^2)=2x#

And, since #5# is a constant,

#d/dx(5)=0#

Thus, the function's derivative is

#18/x+2x+0" "=" "color(blue)(18/x+2x#