Question

I will fan!!
I need help with some calculus questions.

Answer 1

To find y' you have to derive the function with respect to x
\[x = \sin(x+y)\]
\[1 = \cos(x+y) . (1 + y')\]
\[\frac{ 1 }{ \cos(x+y)} = 1 + y'\]
\[\frac{ 1 }{ \cos(x+y)} - 1 = y'\]
\[y' = \frac{ 1 - \cos(x+y) }{ \cos(x+y) }\]

Answer 2

Thank you. I got that right. Could you check this one?

Answer 3

@TrojanPoem

Answer 4

The first, second are wrong:

ddx[f(x)g(x)]=f′(x)g(x)+g′(x)f(x)


The third:

0.5 (f(x))^-0.5 * f'(x) = f'(x) / 2sqrt(fx)

Maybe you noticed something, I didn't.

why do you think the third is wrong ?

Answer 5

I knew it was either the third or none of them. The third one is confusing to me.

Answer 6

The second

derivative of absolute is :\[\frac{ u.u' }{ |u| }\]

In the third:

\[\frac{ d }{ dx } \sqrt{f(x)} = \frac{ d }{ dx } f(x)^{0.5} = 0.5 . f(x)^{0.5 - 1} * f'(x)\]

\[0.5. f(x)^{-0.5} * f'(x) = \frac{ f'(x) }{ 2 \sqrt(fx) }\]

Answer 7

Okay, so the third one is the true statement.

Answer 8

I believe so.

Answer 9

Thank you. it was correct! (:

Answer 10

Any time.