Derivative and Integral of Logarithm Help
Introduction to Derivative and Integral of Logarithm
We begin by noting these facts:
If a > 0 then
Math Note : As always, we can state these last formulas more generally as
We see that
For the second problem, we apply our general formulation with a = 3, u = cos x to obtain
For clarity we set φ( x ) = cot x, φ′ ( x ) = −csc 2 x . Then our integral becomes
Resubstituting the expression for φ( x ) now gives that
You Try It : Evaluate ∫(log 6 ( x 3 )/ x ) dx .
You Try It : Calculate the integral
∫ x · 3 x 2 d x .
Our new ideas about arbitrary exponents and bases now allow us to formulate a general result about derivatives of powers:
For any real exponent a we have
Calculate the derivative of .
You Try It : Calculate ( d/dx )5 sin x−x 2. Calculate (d/dx) x 4π.
Find practice problems and solutions for these concepts at: Transcendental Functions Practice Test.
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