In the following function, let U and R be a variable and V be a constant. Find R'(U). v²R U = - R+V

Q: Use the Product Rule to compute the derivative: # (² + 1)(t +9))|t=13 d ||

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Q: Find the f,fy,fySx and f„ for the following function S(x, y) = y²e»*

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Q: Use the alternative fom of the derivative to find the derivative ot Xo C, if it Exits. f(x) = Ix-6l,…

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Q: Find the derivative of the function. (Sim g(t) = V7 – 4t3 %3D %3D = (?), 6

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

A: We have to find the dydx of the given function.

Q: 1. y = In (x + 5)^(2-x)³ (x + 8) ¹0/6x + 4

A: Solution:-

Q: Find the derivative of the function. f(t) = (6t + 7)2/3

A: Consider the given function below:

Q: Find the derivative of the function.

A: ddx3x2+4x-8x32Apply the Quotient Rule:  fg'=f '·g-g'·fg2=ddx3x2+4x-8x32-ddxx323x2+4x-8x322Solving,…

Q: Use the Product Rule to find the derivative of the function.…

A: We have given; g(s) = √s(s2 + 8)

Q: Decide, whether the function w = z2 + 3z has a derivative (and where) and then find it.

A: Complex number: A number of the form z=x+ιy where x and y are real numbers, is called a complex…

Q: Use the quotient rule to find the derivative of 3w + w4 R (w) = %3D 2w2 + 1

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Q: f(x) = 7e(x²+1) .3 %3D

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Q: Find dy for the following functions. y=6x2

A: We have the given function as   y=6x2 We have to differentiate it

Q: Find the derivative of the function. h(t) = t2(3t + 7)3

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Q: f(x) = 8 f(x) — тх + b f(x) 3 54 + 20х

A: We have to find derivative

Q: Use the product rule to find the derivative of the following. P(Y) = (y¯1 + y-2) (2y -3-7y4) %3D…

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Q: In the given eqaution/s, find the derivative of the function:-   f (t)= (9t + 2)2 /3

A: Consider the given function. ft=9t+223 The chain rule is defined as. dfgtdt=ddtfgtddtgt

Q: Find the derivative of the following function. f(w) 6w +5w+8w 5w? + 8w r(w) =D

A: Given fl(w)=?

Q: Determine whether the following statement is true or false. — [√³] = √f'(x). dx If y = f(x), then

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Q: For the function y = f(x), find f'(a)

A: Here we have, f(x)=x2+5x+2; a=-3 We have to find f'(a)=?

Q: Find the second derivative of the function F(t) = 5tsin(r³).

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Q: For the function y = f(x) = x² − x + 5, x ≥ 0.5, find (ƒ˜¹)'(7) = dy y=7

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Q: find derivative of the function  h(t) = t2(8t + 7)3

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Q: Find the derivative of the function. Re) = (6t + 17)2/3 f '(t) =

A: Given  ft=6t+723 To find the derivative chain rule is used F't=f'gxg'x and the derivative used…

Q: dy Determine or y' of the following functions in terms of x. dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: For the function y df-1 f(x) = a? – x + 2, x > 0.5, find dy y=10 (f-1)'(10).

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Q: Find the derivative of the function. f(t) = (4t2 − 6t + 7)3⁄2

A: Topic:- derivatives

Q: Define what it means by for y f(x) dx

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Q: d By using the definition of the derivative, find the for: dx f(x) = Vx

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Q: For the function f(x,y) = e9xy, find fx and fy. fx = ? fy = ?

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Q: Find the derivative of the function. 8t? f(t): V 5t2 + 4t - 1

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Q: use THE INVERSE FUNCTION RULE TO FIND 1. FOR FACH or THE Fou OWING : (dY 本 y

A: Here we have to find out dy/dx.

Q: Find the derivative of the function. g(t) = (3t2 + 4t − 8)/t3/2

A: The function is gt=3t2+4t-8t3/2.   If a function is of the form, y=fxgx, then the derivative of the…

Q: Find the derivative of the function. s(t) = 44 (8t° -5) %3D s'(1) =D 65

A: st=448t3-565

Q: For the function f(x,y.z) = 3 + 4xy - 5z*, find f,, f, and f,.

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Q: Find the derivative of the function. f(t) = (3t + 18)2/3 f '(t) = 3V31 + 18

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Q: Determine whether the following statementsare true and give an explanation or counterexample.If in…

A: we know that for any given function ∫abfxdx=-∫bafxdx which means given statement is false

Q: 3w + w 5. R(w) = 2u2 +1

A: Solution:GivenR(w)=3w+w42w2+1To find the derivativeFormula:ddxuv=vdudx-udvdxv2

Q: Consider the following function: f(x, y) = 8e*-3y Step 1 of 2: Find fr.

A: a) Given: The given function is, fx,y=8ex-3y The objective is to find fx.…

Q: For each function below, find the derivative using the Chain Rule. If h(z) = 2(2x² + 3)", then h'(x)…

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Q: Consider the following function. f(x, y) = 2a?y + 3xy – 2yt

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Q: Use the limit definition to calculate the derivative of the linear function. g(t) = 8 − 3t

A: Plug the given function in the limit definition

Q: Find the derivative of the function C=25(11q^5−14)^8.

A: According to the differentiation rule the power comes down and reduces by one and then chain rule is…

Q: Find the derivative of the following function. f(w) = 8w° + 5w* + 4w %3D f(w) =D

A: We can find the derivative as below

Q: Find the derivative of the function. -Vx? y = + 36 6 + Vx2 + 36 1 In 36 6x2

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Q: For the function f(x,y)= x^2 +2y^2 Use the first derivative test to determine if the function is…

A: Given function

Q: Find the derivative of the function. g'(t) = g(t) = (8t + 8)² (8t² – 8)−3 -

A: We need to find derivative of given function.

Q: For the function y=inx, find f(e^2)

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Q: Differentiate the following function. r(t) = (4t %3D

A: We have to find out derivative of given functions

Q: For the function f(x,y) = e 6xy, find f, and f,. %3D fy

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