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f(x)=ln(x)cosh(x)-1/2tanh(x)^2−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

ln⁡cosh⁡(x)−12tanh⁡(x)2\ln\cosh\left(x\right)-\frac{1}{2}\tanh\left(x\right)^2

Step-by-step Solution

1

Using the power rule of logarithms: nlog⁡b(a)=log⁡b(an)n\log_b(a)=\log_b(a^n), where nn equals cosh(x)\mathrm{cosh}\left(x\right)

ln⁡(xcosh(x))−12tanh(x)2\ln\left(x^{\mathrm{cosh}\left(x\right)}\right)-\frac{1}{2}\mathrm{tanh}\left(x\right)^2

Final answer to the exercise

ln⁡(xcosh(x))−12tanh(x)2\ln\left(x^{\mathrm{cosh}\left(x\right)}\right)-\frac{1}{2}\mathrm{tanh}\left(x\right)^2

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Similar Questions Solved

derivdef(ln⁡(x))derivdef\left(\ln\left(x\right)\right)

Main Topic: Properties of Logarithms

They are properties that can help us simplify expressions with logarithms.

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lncosh(x)−12 tanh(x)2
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