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Find the derivative of each of the following:~Ze"f() =`_4e"*+3-VS1'g6) =3 tan ' (x) + cot(x' ) 79 = 3f(x) = sing" ) + cos? (x)Find the...

Question

Find the derivative of each of the following:~Ze"f() =`_4e"*+3-VS1'g6) =3 tan ' (x) + cot(x' ) 79 = 3f(x) = sing" ) + cos? (x)Find the derivative of each of the following> = tan(x )sin(+' )J = sin `" (r)fl) = Vx' +3r?g(x) = tan (8x)Find the derivative of each of the following:f(x) = logs (sin x)g(*) = 7*ectr)yek"_Aff() = 4+02Use implicit differentiation t0 find the derivative,Yy=3+4y-2ye = 8

Find the derivative of each of the following: ~Ze" f() =`_4e"*+3-VS1' g6) = 3 tan ' (x) + cot(x' ) 79 = 3 f(x) = sing" ) + cos? (x) Find the derivative of each of the following > = tan(x )sin(+' ) J = sin `" (r) fl) = Vx' +3r? g(x) = tan (8x) Find the derivative of each of the following: f(x) = logs (sin x) g(*) = 7*ectr) yek"_Af f() = 4+02 Use implicit differentiation t0 find the derivative, Yy=3+4y-2y e = 8



Answers

Find the derivatives of the given functions. $$y=\frac{7 \ln 3 x}{e^{2 x}+8}$$

Defined the derivative off given function. F X equals X into e recent the Power seven x We need to apply the product rule. Thus, F dash effects can be evaluated as divide. D X off eggs into e seven eggs plus D by D. X off e seven x in two eggs. Next we evaluate the derivative of each of these expressions. We get one into the race to the power seven X plus seven e raised to the power seven x in two X. Next we simplify to get our final answer, which is he raised to the power seven x into one plus seven x.

Okay, so we see that we were part of the Lex E. So when taking are different, we use our product rule that is the derivative of X is one times remaining term, plus the derivative of E. So that's itself changed A derivative of our inside that seven during times X So simplifying this we get weak, in fact, that I eat in a seven X and then we have one plus seven x on our inside.

Okay, So what Stocks are taking our derivative f prime of X. That's equal to three x ever to over nine minus two times seven. That's 14 x simple. Find this. This is X squid over three money sh 14 X Now we're asked to evaluate F time at three. This is equal to three squared over three minus 14 times three. So one of these streets cancels will offer three minus 14 times three is 42 that's equal to negative 39. So we get f prime at three is equal to negative 30 night.

F of X equal to seven and we have to find the derivative of F of eggs. So here you can see that ffx school to seven. So here seven is a constant. So we know that the day video of constant is zeal. So here we get debatable half of eggs equal to zoo. So it is all final answer.


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