Find the derivative of: 9e 3 cos(- 9x). [Hint: use product rule and chain rule!] Use e^x for e". Now, find the equation of the tangent line to the curve at x = 0. Write your answer in mx + b format. y =

Q: Find the derivative of f(y) = 2 sin y + sin² y and then use it to find all coordinates on the graph…

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Q: find the derivative of tihe unction?

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Q: Calculate the derivative with respect to x of the other variable appearing in the equation. exy =…

A: Given, exy=siny2

Q: Find the second derivative of y=(tan(2pix))^3

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Q: Calculate the derivative with respect to x of the other variable appearing in the equation. tan(x…

A: Given:                tanx2y=x+y3 Derivative with respect to x of the other variable appearing in…

Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: Compute the derivative at the point indicated without using a calculator.           y = sin- 1x,…

A: Given equation is y=sin-1x Rewriting the equation: siny=x Applying derivative with respect to x:…

Q: Calculate the derivative with respect to x of the other variable appearing in the equation. sin(x +…

A: The given equation is  sin(x+y)=x+cosy ...................................(1)  differntiate with…

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

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Q: In y - Р(у) - %3D ey

A: We will use division rule and standard formulas to find required derivatives

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

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Q: Let y = 6Vx. (a) Find using the derivative definition. (b) How fast is y changing when x = 9? %3D…

A: Use the defination of derivative and find the dy/dx dy/dx at point x = 9 gives the slope of tangent…

Q: Determine the derivative of the following functions. 1. y = tanh (8x – 3) 2. y = 2x sinh(6x – 5)

A: Here we will use standard formulas for derivative of inverse hyperbolic functions, product rule of…

Q: Find the first four derivative  if  y= cosx

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Q: Find the derivative with respect to t. y= csc-1(et)

A: Given:

Q: Find the derivative y = cosh(2x)

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Q: Find the slope to the tangent line of the equation y2e2x = 3y+x² at (0,3) Hint: perform implicit…

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Q: y = In(tanh 2x)

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Q: Find an equation of the tangent to the curve x+ Vy = 3 at point (4, 1). [Hint: Use implicit…

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Q: cosx y =-

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Q: Find the derivative of the function. Simplify wherepossible.   y= Sin-1(2x + 1)

A: To find: Derivative of sin-1(2x+1)

Q: Find the slope of the tangent line to the curve x3 + y3 = 4xy at the point (2, 2). Use implicit…

A: According to question given that  We have to calculate the slope of the tangent line to the curve…

Q: (1+x²-1) y = tan²¹ / √₁+x²

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Q: 1. cos(xy) + secy = 5

A: Differentiation is the process of determining the derivative also known as the derived function. one…

Q: Compute the derivative at the point indicated without using a calculator.             y = tan-1 x ,…

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Q: Find the second derivative of y = cot 3x

A: To differentiate the function in the first derivative as y' ordydx  and the second derivative as y''…

Q: Find the derivative of y with respect te X /3 %3D

A: Finding dy/dx

Q: Compute the derivative using derivative rules. y = cos(te- 2t)

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Q: Find the derivative of y = arccos 4x with respect to x.

A: Given that: y=arccos4x

Q: find the derivative of the funciton y=xe^(5x)

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Q: Find the derivative of the functiony=tan^2(6x)

A: we have to find derivative of f(x)we will use following rules

Q: Find the derivative of the function defined by the equation x+y=arctan(xy).

A: To find the derivative of the given function.

Q: Find the derivative. Simplify where possible. y =e cosh 3x

A: Given: y=ecosh3x

Q: Use the derivative implicitly to find the slope of the tangent line at the point ,0), Suppose y is a…

A: Given- siny+cosx=12 To Find- The slope of the above expression at the given point π3,0.

Q: Find the derivative of y = sin (cot(3x)) %3D

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Q: Find derivative of y=cos(7x).

A: The given function is

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec-1

A: Let, z=(2x+3)/5   We differentiate using the chain rule

Q: Find the derivative of y with respect to the appropriate variable. y = cosh12 x+ 5

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Q: Find an equation of the tangent line to x2 +xy – y³ = 7 at the point (3,2). (You must use implicit…

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Q: y = cos /sin ( tan tx

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Q: есх Find the derivative of y = Arccot (tan(esec*)) in its simplest form secr

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Q: calculate the derivative with respect to x.

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Q: Find the derivative of y with respect to x for y=2x   ???

A: y=2x

Q: e) Now, deduce the derivative of y = tan(r) by applying the Quotient Rule.

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Q: find the derivative of y with respect to the givenindependent variable. y = 2x

A: y=2x

Q: Find the derivative using the definition 1- y = vx -1

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Q: b) y = cosh(2Vx+1)

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Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

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Q: find the derivative of y with respect to the givenindependent variable. y = 3-x

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