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Computing Derivatives

Computing Derivatives

At a Glance - More Derivatives of Logarithms

Whenever possible, rewrite a function so it looks good before taking its derivative.

Any logarithm loga can be written as

This allows us to find derivatives of logarithms in bases besides e.

We also know enough now to find derivatives of things like

f(x) = ln (x2).

We can bring down the exponent to find

f(x) = 2 ln x,

and we know how to find the derivative of this:

Example 1

Find the derivative of  f(x) = log10 x.


Example 2

Find the derivative of f(x) = logx2.


Exercise 1

Find the derivative of the function.

  • f(x) = log9 x

Exercise 2

Find the derivative of the function.

  • g(x) = log2 x

Exercise 3

Find the derivative of the function.

  • h(x) = ln x10

Exercise 4

Find the derivative of the function.

  • j(x) = logx4 

Exercise 5

Find the derivative of the function.

  • k(x) = log5(x3)

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