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

Q: Find the derivative of the function. q= V 16r -r 1 OA. 2/16-7r 9. O B. 16r-r 16 – 7.° c. 2 16r-r OD.…

A: q=16r-r7

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

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

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: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

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

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: FIND THE SECOND DERIVATIVE OF THE FOLLOWING IN ITS SIMPLIFIED FORM. x = t/t-1 , y = t2/t2-1

A:

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

A: The derivative of the function is the rate of change of the function. A composite function is…

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: Find the two first-order derivatives of the function f(x, y) = 2xy² – x² +y* You must show work.

A: ∂f/∂x = fx(x,y) = d/dx [2xy2 - x2 + y4]                       = 2y2 - 2x ∂f/∂x = fx(x,y) = 2(y2 -…

Q: Find the derivative of y with respect to x. 6х + 11 y = - csc 7 O A. 42 |6x + 11|V(6x + 11)2 – 49 O…

A: ddx(cosec-1x)=-1xx2-1

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: Assume that x and y are both differentiable functions of t and that they are related by the given…

A:

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: The value of the second derivative of y = f(x) at its point of inflection is A. 1 B. 0 C. -1 D. 2

A: An point of inflection, is a point on a curve where the curve crosses its tangent at that point.

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: Find the second derivative of the function. t° + 9t +5

A:

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

A:

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

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: 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: 1. For the function f(x) = 3x² + 8x – 7, (a). Find the slope of the tangent line at x = 2. . (b).…

A:

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

A:

Q: 1. Find the derivative of the function y = (x² – 1) (2x² – 3). | 2. Differentiate g (x) = x+1l x+2 °…

A:

Q: 5. x= y= t2-1

A:

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

A:

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

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: 2 2 X = 1+t2 y=r(1+t?)

A: To find second derivative of given function.

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 7x + 8y.…

A: Directional derivative: - The partial derivatives of f give the slopes ∂f∂x in the positive…

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. 4x° +8 y = y' =O

A: We have to find