Question 4d 4. Recall that 4 (In z) = 1, () =e², and that (a=) =a* In a, where a >0 is a constant(as deduced in class). Apply the Power Rule, combined to the Constant Multiple Rule, theSum Rule, the Difference Rule, the Product Rule, the Quotient Rule, and/or the ChainRule to compute the derivative of each one of the following functions:a)f(2) = VEb)S(2) = V/#+4z –5c)f(2) = In (z² + 7)d)f(z) = In (In z)e)f(z) = /3sin(5z)f)sin zf(2) =cos zBring your ansuer to the simplest possible form.g)S(2) = e==h)f(<) = 2* + !i)f(z) = z(4*) +7j)S(2) = V25. Now, explain the difference between the following two examples from the point of view ofdifferentiation:d(29)s00 Panddz cos"(z)Compute explicitly each one of them.6. Based on our class discussions, recall that some functions are defined implicitly by a relationbetween z and y such as z+y = 25. In such cases, differentiating with respect to z both sideshelps us compute . We should be careful, however, with the Chain Rule that needs to be appliedin the way. That is, if y is assumed to be a function of z, then(1²Y = 2y(3/')(e®Y = (e®)v/and so on.

Name: Question 4d 4. Recall that 4 (In z) = 1, () =e², and that (a=) =a* In
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Question 4d 4. Recall that 4 (In z) = 1, () =e², and that (a=) =a* In a, where a >0 is a constant(as deduced in class). Apply the Power Rule, combined to the Constant Multiple Rule, theSum Rule, the Difference Rule, the Product Rule, the Quotient Rul