Difference between revisions of "Derivatives of Logarithmic and Exponential Functions"

Latest revision as of 14:27, 15 September 2021

Natural log of $x$ : $(ln(x))'={1 \over x}*(x)'$
log of $x$ : $(log_{a}x^{z})'=({lnx^{z} \over lna})'={1 \over ln_{a}}(lnx^{z})'={zx^{z-1} \over ln{a*x^{z}}}$

No meter what you can use this equation to get the answer.

$(ln(x^{n}))'={n \over x}$

$(log_{a}x^{z})'={z \over ln{a*x}}$

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 #Natural log of <math>x</math> : <math>(ln(x))'= {1 \over x} * (x)' </math>
-#log of <math>x</math> : <math>(log_a x^z)' = ({ln x^z \over ln  a})'={1 \over ln_a}(ln x^z)'= {z x^{z-1} \over ln       {a*x^z}} </math>
+#log of <math>x</math> : <math>(log_a x^z)' = ({ln x^z \over ln  a})'={1 \over ln_a}(ln x^z)'= {z x^{z-1} \over ln   {a*x^z}} </math>
+<noinclude>
+==Natural log==
+====equations it may be help full====
+No meter what you can use this equation to get the answer.
+<math>(ln(x^n))'= {n \over x} </math>
+==log(Not Natural log)==
+====equations it may be help full====
+<math>(log_a x^z)' = {z\over ln   {a*x}} </math>
+</noinclude>