Derivative of the natural logarithm by using the

Reference no: EM13357249

Derivative of the natural logarithm by using the fundamental theorem of calculus.

To find the derivative of y = ln x. This solution below is not complete. It would be useful to use the Fundamental Theorem of Calculus here.
Integral(1, x) 1/t dt = F(x) - F(1), where F(x) is the antiderivative of 1/x (so F\'(x) = 1/x).
ln(x) = Integral(1,x) 1/t dt = F(x) - F(1)
Now take the derivative:
d/dx(ln(x)) = d/dx(F(x) - F(1)).
Continue to show that d/dx(ln(x)) = 1/x.

Reference no: EM13357249

Questions Cloud

Series convergencea prove using the definition that the : series convergence.a prove using the definition that the following sequence convergerradicnn 1b using the definition

Calculus - sequences and series tests of convergenceuse the : calculus - sequences and series tests of convergence.use the root test to show that a geometric series converges only

Integration by parts methodusing integration by parts : integration by parts method.using integration by parts evaluate nbspintx cos3x dx. check your answer by taking the

Summation and proof using mathematical inductionsuppose : summation and proof using mathematical induction.suppose that xn is a sequence of positive real numbers for which the

Derivative of the natural logarithm by using the : derivative of the natural logarithm by using the fundamental theorem of calculus.to find the derivative ofnbspynbsp

Determine accumulated rates of change using definite : determine accumulated rates of change using definite integral.give another example with solutions to emphasize that the

Change into symbolic notationtranslate the following into : change into symbolic notation.translate the following into symbolic notation. use for negation amp for conjunction v

Find the nth term of the given sequencesnbsp1write out the : find the nth term of the given sequences.nbsp1.write out the nth term for the continuation of the

Evaluate the coordinate of centroid using multiple integral : evaluate the coordinate of centroid using multiple integral methodlet t be the region inside the sphere x2nbsp y2nbsp

User Account

All Pages