4 For the function y = f(x) = 1+ x2 a. Find the slope of the line tangent to its inverse function at the point P(2, 1): m = b. Find the equation of the line tangent to the inverse function at the point P(2, 1): y =

Q: The function y(x) satisfies the equation 25x2-10y+1/2y2=25. What is the value of the second…

A: 25x2-10y+12y2=25 Differentiating with respect to x, we get…

Q: Find the 1st and 2nd derivative of this function: x=(t-2)5/2  y=t3-5

A: We will differentiate the function twice to get the first and second derivatives as follows while…

Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)? A) x…

A:

Q: Find the derivative of the function. f(x) = V 5x + 4

A: Question number 1,Given,          fx=5x+4

Q: Find the derivative of the given function. 275 y= 22+4 e -3x %3D

A:

Q: use the Chain Rule to find the derivative. y = (t2 + 3t + 1)−5/2

A: Given: y=t2+3t+1-52 Let, t2+3t+1=u Then, by using the chain rule dydt can be found out as,…

Q: Find the derivative of the function. f(t) = t2/3 − t1/3 + 4

A:

Q: Take the derivative of  (x+y)3=3x-4y+5 with respect to the variable t . Do not rearrange and move…

A: NOTE: Refresh your page if you can't see any equations. . take derivative on both sides with…

Q: For the function f(X) = ax3 +ba2 +cx, find the second derivative, f"(X). Here a,b and c are…

A: Given Function,F(x) = ax3 + ba2 + cx

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A:

Q: Find the first, second and third derivative of the given function. -4 7. f(x) = (t+2)?

A:

Q: Find the equation of the tangent line at y = 0, given the inverse function x (3y + 2)(y+1)2. x - 7y…

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Q: Find the derivative of the function. G(y) =Y - 1)5 (y2 + 2y)º

A:

Q: For f(t) = (2x − 3)3, find the equation of the tangent line at (a)  x = 0 (b)  x = 2

A: We have to find tangent line to f(x) at two different points, f(x) is given .at x=2 y=1at x=0 y=-27

Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Given,            K(t) = 4.4t3 - 8t2 + 5t - 11             t(x)  = ln x              dtdx = ddxln x…

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A: The given functions are

Q: Find the derivative of the function. f(t)=(1+t^1/2)(4t^2-5)

A:

Q: Iff (x,y)=xcosy+ye*,find the second order derivative ô²f_ ô²f_ôf_ ô²f and дхду ôx² 'ôyôx' ôy²

A:

Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Obtain the composite function as,

Q: Find the derivative of the function .

A: The given function is  ft=t23-t13+4

Q: For the pair of functions, find the derivative of the composite function  f(t(x))  in terms of one…

A: Given  f(t)=2t and t(x)=x2+6x Now dfdx=dfdt·dtdx

Q: Determine the derivative of the given function: ソ=c 3 y = e x2

A:

Q: B. Find the indicated derivative. -4 1. у: 2. x2 – 4y2 = 5; y" iy(3)

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Q: Find the equation of the tangent line at y = 0. given the inverse function x = (3y + 2Xy + 1)2. ...…

A: Equation of tangent

Q: Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

A: Explanation:

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A: Given:     To determine: dc/dt

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

A:

Q: Find the derivative of the function. f(t) = (9t + 2)2/3

A: We have to find the derivative of the function f(t)=9t+223.

Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Consider the given pair of functions k(t) = 4.8t3 – 12t2 + 10t – 11;  t(x) = ln x

Q: Find the derivative of the function. f(x) = e!/(9x) f'(x) = %3D

A:

Q: Find the equation of the tangent line at y = 0, given the inverse function x = (3y + 2)(y + 1)?. A)…

A: To find the equation of tangent line

Q: For the pair of functions, find the derivative of the composite function  f(t(x))  in terms of one…

A: Given: ft=t2+2; tx=ex To Find: dfdx Concept: i. ddxfgx=f'gx·g'xii.  ddxeax=aeax

Q: Find the second derivative of the function. f(t) = t(t2 + 3)3 f"(t)

A: (uv)'= u.v' + u'.v

Q: For the pair of functions, find the derivative of the composite function  f(t(x)  in terms of one…

A:

Q: Find the second derivative of the function F(t) = 4tsin(r4).

A:

Q: Find the derivative of the function. g(t) = 1/(√t2 − 2)

A: The given function is ,gt=1t2-2. To find the derivative of the given function. Solution: The…

Q: I) Find the derivative of each function a)y =x' In x b)y = 4x'e c)y = eF

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Q: Find the derivative of the function.

A:

Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

A:

Q: Given the function f(x, y) = x - y' + 2xy. Determine the derivative a?f/ əx² .

A: Find your answer below

Q: For  f(x)=(2x−3)3, find the equation of the tangent line at x=0 and x=2.

A: Given the equation of the curve, f(x)= (2x-3)3 To find the equation of the tangent line at x=0 and…

Q: Q3. Find the derivatives of the functions 2x + 5 a) y b) w = (2x – 7)(x + 5) Зх — 2 5x + 1 с) и 2 Vx

A: We have to find the derivative of the following functions a)  y=2x+53x-2 b) w=(2x-7)-1(x+5) c)…

Q: Obtain the derivative of the following functions: a2 + x3 + 2y = y² 10. Solve for the derivative of…

A:

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

A: Given:f(t)=5lm(t),t(x)=5x3-4x2+9x

Q: Calculate the second derivative of the function y = f (x) defined by the equation x³+ y³ +3xy+ 3y² +…

A: Explanation:

Q: Find the derivative of the function.   y=3e^8t+3

A: Given function;   Taking the first derivative;

Q: for the function y=f(x)=x+lnx, find the derivative of the inverse function

A:

Q: Find an equation of the line tangent to x = t^2 −1, y = t^3 +t at the point corresponding to t = 2.

A: