Question

please help ASAP calculus

Answer 1

i think 3 is the easiest to figure out, if anyone can help id much appreciate it

Answer 2

@Hero @HuskyNation

Answer 3

3.) Find dy/dx for y = 3cos(x) + csc(x).

3sin(x) – csc^2(x)
–3sin(x) – csc(x)cot(x)
3cos(x) – csc(x)cot(x)
3sin(x) – csc(x)

First, a review:

The derivative of cos x is -sin x. With the constant coefficient 3 in the picture, we have 3cos x. The derivative (dy/dx) of that is -3sin x.

The derivative dy/dx of csc x is negative something. Can you find the formula?


With that much behind us, can you now choose the correct answer from below?

3.) Find dy/dx for y = 3cos(x) + csc(x).

3sin(x) – csc^2(x)
–3sin(x) – csc(x)cot(x)
3cos(x) – csc(x)cot(x)
3sin(x) – csc(x)

Answer 4

Regarding:

"Givenf of x equals 5 times x minus 6 for x less than 4, equals x squared minus 2 for x between 4 and 6 inclusive, and equals 4 times x plus 10 for x greater than 6 find f ′(x) and give its domain." This is a real stinker to read. Please get into the habit of translating these functions into the proper symbols:

f(x)=5x-6 only for x values smaller than 4
= x^2-2 only for x between 4 and 6, including x=4 and x=6
= 4x + 10 for x greater than 6

This is called a "piecewise function," because it's defined differently on each of three intervals. Please note that the derivative does not exist where the first interval ends and the second one begins, and that it does not exist where the 2nd interval ends and the third one begins. So, you MUST indicate these discontinuities using ) or ( instead of ] or [.

The deriv. of 5x-6 is merely 5. This is true ONLY for (-infinity,4).
What is the derivative of x^2-2? Note that this is true ONLY for [4,6].
What is the deriv. of 4x+10? Note that this is true only for (4, infinity).

Answer 5

@mathmale would #3 be B then??

Answer 6

@Hero

Answer 7

"–3sin(x) – csc(x)cot(x)" is correct. Be sure you know how to obtain that result by applying rules of differentiation.

Answer 8

it seems as if we always miss each other! and ok, thank you!

Answer 9

@mathmale im not sure yet about the other 2 though... if you could expound more on that id be grateful

Answer 10

@mathmale also, would the last one you commented on be D, then?? (the Given f... question)

Answer 11

??

Answer 12

This is in regard to #3:

"–3sin(x) – csc(x)cot(x)" is correct. Be sure you know how to obtain that result by applying rules of differentiation.

Answer 13

Regarding #2: I did respond in depth; did you see my post (above)? Happy to clarify anything about the problem or about my explanation that's not clear to you.

Answer 14

" the derivative with respect to x of the quotient of the quantity g of x and f(x) equals the quotient f of x times g prime of x minus g of x times f prime of x and the square of f of x

If f and g are differentiable, then the derivative with respect to x of the product of f of x and g of x equals the product of f prime of x and g prime of x.

If f and g are differentiable, then the derivative with respect to x of the square root of f of x equals the quotient of f of x and 2 times the square root of f prime of x.

None of these statements are false."


START HERE => The first answer, "the derivative with respect to x of the quotient of the quantity g of x and f(x) equals the quotient f of x times g prime of x minus g of x times f prime of x and the square of f of x" is correct. I strongly suggest that you look up Quotient Rule and compare what you find to what this statement says.

Answer 15

CONTINUE HERE =>

Answer 16

There's a fair number of words to wade through in the first question. Having been paddling, I think that all the statements are true, so none are false. I think the last one is a wordy way of describing differentiating a function of a function.