dy of the following functions. [1 mark ] da A5) Find (a) y = sec(4x²) [ 0.25 mark ] (b)y = sin4x + cos4x [0.5 mark ] (c) y = cot (V4- x2) [ 0.25 mark]

Q: dy For the function dt 5 cos t, the third order derivative dt is O 5 cost O 5 sint O -5 sint O -5…

A: Given  dydt=5 cos t          ............ (1) We have to calculate the third-order derivative of y…

Q: Find the differential of the function. y = theta3 sin(9theta)   dy=?

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Q: Find the derivative. sin 0 d. 1 dx 1- x2 de A. tan 0 B. sec 0 C. cot0 O D. cos 0

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Q: Q2) find the slop for the tangent of the function f (x) sin(xcos(x)) at x = 2n. %3D

A: To find the slope of the tangent of the function fx=sinxcosx at x=2π. Solution: The slope of a…

Q: 4iven oc= sin34 ond y= cos 34, find the follo wing derivatives as functions of t dy doc

A:

Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: dy Use implicit differentiation to determine dz given the equation zy + cos(z) = e".

A:

Q: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

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Q: (2 – 4t) sin() tan(2r) V17 – cos(2nt) Find the equation of the line tangent to the graph of f at r =…

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Q: Q5: Find dy dx (1) In(x - y) = xy + y³; for the following functions: (2) y = tan³√/cot(7x);

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Q: Find dy/dx for following functions. 1) y = csc-(e2lnx) + sin-1(2lnv3x)

A: it is given that,  y=csc-1e2lnx2+sin-1(2ln3x) we have to find dydx=?

Q: nswer two only: [25] M W Find the equation for tangent to the curve y = x + cos(2x²) at x = 2.

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: nd the equation of the tangent to the curve y = 2 sin x+ cos 2x at the point x= 7.

A: equation of line at point (a,b)  is given by    y-b = m (x-a)  Where m is the slope of tangent  As…

Q: Find the derivative. sin t du 4-u? di cost OA. 4- sin?1 O B. cos t(4- sin ?1) OC. 4- sint - cost O…

A: We need to find the integration of given expression.

Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

A:

Q: dy For the function dt 8 cos t, the third d³y order derivative is dt3 8 cos t -8 sin t cos t 8 sin t…

A: dy/dt = 8cost

Q: Q2\ find y' when y = Vx² • sin2x + cosh 5x %3D

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: dy Find for the following function. dx 5- cos x y = 6+ cos X

A: To determine the first order derivative of the function.

Q: Two particles start at the origin and move along the x-axis. For, 0 <t< 10 their respective position…

A: Given, x1=sint , x2=e-2t-1 ,0≤t≤10 To find the velocity, Differentiate with respect to t we get,…

Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

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Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x =…

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Q: dy Find for the following function dx 5 cos x y%3D 1- sin x

A: The given function is, y=5 cosx1-sinx

Q: Q3: dy\dx of f(x)= tan x cot x is

A:

Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + ex²+x -

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Q: For the following functions, state the domain of y, find dy dx and its domain. 279. y=sin-¹(x²) 280.…

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y =…

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again…

Q: What is the equation of the line tangent to the curve e+cos(x) =1 at the point ,02 + cos Ay= y=x-…

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Q: Q3: dy\dx off(x)= tan x cot x is

A: Given,    f(x) = tan(x) cot(x)         = 1   As we know, inverse of tan(x) is cot(x).

Q: Use implicit differentiation to determine expressions for dy/dx in the following: i) 5ex2cos y=e2y…

A: Given equations are, i. 5ex2cosy=e2ysinx ii. sin2x-4sinx cosy+tany=0

Q: Find dy/dx for the following function y = cosh[sin-'(x²Inx)]

A: Please refer to the image below.

Q: Q2- Find for the following function :- dx 1- y = sinh-(tan x) – tanh-1(sin x)

A: We will differentiate using direct formula and chain rule.

Q: Q5// Evahate dx 1- J- V&r-x 6co(3x2) dx dx sin - sinx

A:

Q: dy Find for the following function de sin 0 y : ACos 0-1.

A: We have to find derivative

Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³; (2)y=tan³ √/cot(7x); cash? -nh.…

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Q: Find the second of the finchion, ç x) = cos e derivative f (x) (x %3D %3D

A: Consider the given function: f(x)=xcosx The first derivative is calculated using the product rule.…

Q: Find the slope of the tangent line to the path of a carnival ride x 7 cos() + sin(7t), y = 7 sin() +…

A: Given  x=7cos(t)+sin(7t) y=7sin(t)+cos(7t) We need to find the slope of tangent at t=0

Q: b) Differentiate the function y= sinx-xcos.rwith respect to x.

A: Given: y=sinx-x cosx

Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: 16. Use Implicit Differentiation to find an expression for dy/dx given r*y² + cos(y) = 1. %3D

A: Given: x3y2+cosy=1   We know that; The Sum rule: f±g'=f'±g' The Product rule: f·g'=f'·g+f·g' The…

Q: dy Q2- Find for the following function :- dx 1- y = sinh-1(tan x) – tanh-1(sin x)

A: Given that      y = sinh-1(tanx) - tanh-1(sinx) We have to find dy/dx.

Q: b. y = Vxe2x cos x хе2х сos

A: Given: y=x e2x cos x To determine: Derivative of the given function

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³ ; (4) y = x sinh 2x -cosh 2x (2) y…

A: We need to find derivative. As per Bartleby's guidelines we can solve one question from multiple…

Q: 3- Use implicit differentiation to find dy 2 B. Xx-Cot (xy) y Sin f )=1-xy 2

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Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: For what value(s) of x in the interval -15 sxs -5 will the sinusoidal function shown below have a…

A: By definition, a function is a special case of a relation between the members of two sets. It is a…