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Given: Let f(x.Y.z) = x. (12) f; x(ln x); (B) x[y(ln x)I; (C) xT(yz)x]; (D)x[z(ln x)I; (E) None of these....

Question

Given: Let f(x.Y.z) = x. (12) f; x(ln x); (B) x[y(ln x)I; (C) xT(yz)x]; (D)x[z(ln x)I; (E) None of these.

Given: Let f(x.Y.z) = x. (12) f; x(ln x); (B) x[y(ln x)I; (C) xT(yz)x]; (D)x[z(ln x)I; (E) None of these.



Answers

If $f(x)=3-2 x+x^{2},$ then $\frac{f(x+t)-f(x)}{t}=$ (A) $t^{2}+2 x t-2 t$ (B) $x^{2} t^{2}-2 x t+3$ (C) $t+2 x-2$ (D) $2 x-2$ (E) none of the above

We have about the number 114 in which we have been provided FX equal to ex Esquire. Menstrual. Sorry. Excess squared minus 12. And we need to find the value off F off 12 which will be 12 square minus trail. That is 1 44 minus 12. That is 1 30 to so after 12 days, 1 30 True wonder. Ditto so. Part B F A. If a way can be found out by plugging in the value off X equal to a in or is nearly question Esquire minus trail. Thank you.

We need to evaluate the function F. Of X when x is equal to negative A. So we have F. Of negative A. So we have negative A squared minus three times negative A. This becomes positive A squared plus three A. So the function F evaluated at negative A is equal to a squared plus three A.

In this problem, we directly compute F two is equal to four times two thirds of minus five times two. So this is four times 8 -10. So this is 30-10, will be 12 and then f minus Two will be four times -2 to deserve -5 times -2. And this will be minus hold time eight plus 10, Echo to -30 to plus 10 will be minus okay, F A is equal to four times a ser minus five. A and f minus eight. It will be four times minus a third time minus five times minus A. So this will be in minus 48 sir, first friday. And also a side information is this function contains all the old like a degree of X. There's no even degrees. So this function, this polynomial is even function. So, so sorry, it's our function. But the artist function we know FA is always equal to minors F -8. And you can use this to checks whether to do this image to check for your answers.

The topic of this question is the product rule. All we want to do in this question is pretty much uh describe what the product rule is. So for example, say you have a function capital F. Of X. And that function is a product. Well, the product of two other functions be FX and cfx. Yeah. Now the derivative are, sorry, the product rule for differentiation tells us that the derivative of this F, which is a product of two functions, derivative of this product function is given by this formula. Yeah. The derivative of B multiplied by C. Oh yeah. Close B times the derivative of seat. Yeah. And this is all that. The product rule is. It's just a formula that tells us how to differentiate a product of two functions, which is also a function has functioned as a product of two different functions. BNC has a derivative given by the prime C plus B times C. Prime. That brings us to the end of this video and thank you for watching


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