If sin-r= In y, show that UTM dy (1-2) = y. dr

Q: Use a calculator to compute sinhx and coshx for x = -3, 0, 5.

A: We use a calculator to find the values.

Q: tanX Differentiate with respect toX logs sin?x

A: Use the following formulas to calculate the derivative. logab=lnblnaddxtanx=sec2xddxcsc x=-csc x·…

Q: Find dy/dx if 3 (cos y) (sin x) = y

A:

Q: sinx + sinx CScx + 1 CScx - 1

A: Use following trigonometric identities  1. cscx = 1sinx 2.(csc2x - cot2x) =1

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

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Q: Show that for x > 0, sin ¹x+cos -1 X = FIN 2

A:

Q: Evaluate LE, sin't dt (Identity needed here)

A: Given integration is ∫-π3π3sin2(t)dt We know that,…

Q: Let y = cot (csc2x/x3+5). Find

A:

Q: Consider the function y=sin0, where 0=u+v. Suppose that u = v. Show how the Sum and Difference…

A: We will see the ans in next step

Q: Show that tan-1 ( 1/v ) = π/2 - tan-1 v, if v > 0.

A: To prove tan-11v=π2-tan-1v, let  x=tan-1v then tan x=v1tan x=1v Since  tanx=1cotxcotx=1v ⋯ (1)

Q: etermine the form that would make f sin () cos () sin(0) de

A: We have to determine the form of the given indefinite integral

Q: y' = 2 - sin t

A: Given that y'=2-sint. solve the above differential equation as follows.

Q: Let 5 sin⁡x+ 7 cos⁡ y=6. dy/dx= d^2y/dx^2

A: 5sinx+7cosy=6Differentiate w.r.t x5cosx-7sinydydx=05cosx=7sinydydxdydx=5cosx7siny

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: de 8)

A: we have to substitute 3x = u

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: Differentiate  (sin 2t)/t.

A: ft=sin2tt

Q: Find f'(z) if f(z) = 8 cos(z) + 9 sin(z). Answer

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Q: Find all Second partial derivatives fcx.y)- Sin?Cmx+ny)

A: Given that, f(x, y) = sin2(mx + ny) we have to find second partial derivative with respect to x and…