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swat32
3 years ago
11

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
natulia [17]3 years ago
3 0

Answer:

g'(x)=\frac{2e^x-e^{-\frac{x}{2}}}{2(e^x+e^{-\frac{x}{2}})}

Step-by-step explanation:

We are given that a function

g(x)=ln(e^x+e^{-\frac{x}{2}})

We have to find the derivative of function

Differentiate w.r.t x

g'(x)=\frac{1}{e^x+e^{-\frac{x}{2}}}\times (e^x+e^{-\frac{x}{2}}\times (-\frac{1}{2}))

By using formula

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{d e^x}{dx}=e^x

g'(x)=\frac{e^x-\frac{e^{-\frac{x}{2}}}{2}}{e^x+e^{-\frac{x}{2}}}

Hence, the derivative function

g'(x)=\frac{2e^x-e^{-\frac{x}{2}}}{2(e^x+e^{-\frac{x}{2}})}

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