y = cos x means that x = for 0 ≤y ≤t.

Q: I understand that the derivative of cosx is -sinx, but I need to show the work using trig…

A: We have to find the derivative of cos(x) by using definition of derivative by limit.

Q: For the following exercises, find functions. 175. y=x²-secx + 1 176 177. y = x² cotx 179. y = Sec.x…

A: Use rule of differentiation (u.v) form  and (u/v) form as I have done in solution

Q: B)ls w = Ze² analytical function or not?

A:

Q: 20. Show that -V3 is in the range of the tangent function by finding an angle 0 for which tan 0 =…

A: Given:  tan θ = -3To Find : The value of θTo Show:  -3 is in the range of the tangent…

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

A:

Q: DO NOT include spaces in between characters. Determine the domain of y = sin (x – 1).

A: To find the domain of y=sin-1x-1

Q: /hich functions are continuous for all real numbers? i.y = xi ii. y = e* iii. y = tan x

A:

Q: Find the derivatives of each of the following functions f(x)=-2 sinx b) y=-cos²x c) y = 3x sin x d)…

A: find the dervative

Q: Find y^" when y=sin(ax)*cos(bx),a,b any real numbers. Find y" when y = sin(ax) · cos(bx), when a, b…

A: The given function is: y=sin(ax)cos(bx) So, y'=sin(ax)ddx(cos bx)+cos(bx)ddx(sin(ax))…

Q: For cos2(xy) =, evaluate y' when x = 4

A: Given that: cos2(xy)=14

Q: Test the function defined by f(x, y) = exp 2x-y x+2y -cos 2x-y x + 2y for its homogeneity. If it is

A: Given: The function is fx,y=exp2x-yx+2y-cos2x-yx+2y. To check: The given function is homogenous or…

Q: dy for the following implicit functions : dx Find a) x+4xア-ア 5y =3 3べ+5y'x"+4\」 (ans.: 2.x 10xy-y

A:

Q: 2. Determine where y=sin is continuous.

A: Please see the below picture for detailed solution.

Q: O x = 4 ve Find all points where the function is discontinuous. e

A:

Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C.…

A:

Q: How do the slopes of the lines tangent to the graph of y = tan-1 x behave as x S ∞?

A: The slope of the line tangent to the graph of y=tan-1x  at a point is the derivative of the function…

Q: Determine the equation of the line that is tangent to y = 2 tan x, where x = 4. O-4x + y - (2-) = 0…

A:

Q: Differentiate the following function: u' = = u = √√ +² +6√√√+³

A: Differentiate both sides with respect to 't'

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: dz dz and ду Suppose z is a function of r and y, and tan Vy? + x2 = z"e6y. Solve for

A: