"- ts' = 1- sin (t) (4) + xy" = e* dx 6x '– y²Iny = (y')²

Differentiate y = xe у'3

which of the following equation is a variable separable DE? |а. (х + хx^2y) dy %3 b. (х + у) dx- 2y dy с. 2у dx d.y^2 dx + (2х- 3у) dy (2х + ху^2) dx = 0 (х^2 + 1) dy = 0

(2х + 1)у? y' = y2 - 1

A cable hangs between two poles of equal height and 30 feet apart. Set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. The height (in feet) of the cable at position x is h(x) = 17cosh(x/17) where cosh(x) = (e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is ______ feet long?

I don't understand why derivative of e^iax=(e^iax)/ia. Can you please explain it to me? Thank you

a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t, where x is the horizontal direction and y is the upward direction. the projectile lands after  a. 16 seconds b. 8 seconds c. 4seconds

let c1=(e^-4t,sin(t),3t^3) c2= (e^4t,cos(-5t),3t^3) d/dt[c1 dot c2]=? d/dt[c1 cross c2)=?

Differentiate y=sin'x- cos'x %3D sin’x – cos'x A. 3sin x cos x (sinx - cos X) B. 3stn x coS x (sinx + cOS X) C. sin x cos x (sinx + cosx) D. 3sin x (sinx + cos x)

CORRECT to find y'(x). vle) = (In2=)× (ain u) d d d d v'(x) = (In 2) x (sin u) dx v'(x) = -(In 2r) x dx -(sin) 2x ) × du ..... .... d y'(z) = da d v(4) = sin (In2) + In 2z (sin) -(In 2) x (sin u) d y'(x) = sin- dx dr du ..... ...