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

Answer 1

#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#

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Answer 2

Charles Anctil

To find the derivative of (18 \ln(x) + x^2 + 5), you apply the rules of differentiation.

The derivative of (18 \ln(x)) is (\frac{18}{x}) by the derivative of natural logarithm rule.

The derivative of (x^2) is (2x) by the power rule.

The derivative of a constant, such as (5), is (0).

So, putting it all together, the derivative of (18 \ln(x) + x^2 + 5) is (\frac{18}{x} + 2x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.