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# Find the derivative of (sin x)cos x + (cos x)sin x

Find the derivative of the function Rewrite each of the exponentials in the expression for using the definition of the exponential function, Now, we take the derivative directly using the chain rule and the formula for the derivative of the exponential function # Find the derivative of (log x)x / xlog x

Find the derivative of the function To take this derivative we want to use logarithmic differentiation. To that end, take the logarithm of both sides of the equation for , Now, we can differentiate both sides to obtain, # Find the derivative of xlog x

Find the derivative of the function To find this derivative we want to use logarithmic differentiation. Take the logarithm of both sides, Then differentiating both sides of the equation (and using the chain rule for the derivative on the right hand side), Substituting back in our original function we obtain # Find the derivative of (log x)x

Find the derivative of the following function: We want to use logarithmic differentiation, so first take the logarithm of both sides, Then differentiating both sides we have # Find the derivative of log (ex + (1+e2x)1/2)

Find the derivative of the following function: We compute using the chain rule and the formulas for derivatives of logarithms and exponentials, # Find the derivative of log (log (log x))

Find the derivative of the following function: Here we apply the chain rule (carefully), # Find the derivative of xx

Find the derivative of the following function: We can take differentiate using logarithmic differentiation. First, take the logarithm of both sides, Then, differentiating we obtain # Find the derivative of elog x

Find the derivative of the following function: Since the derivative is given by We could check this if we wanted by using the chain rule and the derivative of the exponential on the original formula for , # Make a table of log n for n = 2,3, …, 10

Using the previous four exercises (#1, #2, #3, #4) make a table of the values of for .

The table is as follows. # Calculate an approximation of log 7 in terms of log 5

With reference to the previous three exercises (here, here, and here) use to calculate in terms of . Obtain the qpproximation Letting we have Therefore, we apply Theorem 6.5, 