Differentiate the function f(t) = t (5t + 2).

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

A:

Q: Find the average rate of change of f(x)=3x2 +2x−2 on the interval [2,t].

A: Consider the function f ( x ) on the interval [ 2,t ],

Q: What is the derivative of f(x) = x² +x² a +2 where a is a constant ? xa+2

A: We write f(x) using exponents f(x)=x7+x2+a+2xa+2f(x)=x7+x2+(a+2)x-(a+2)

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

A: Here given y = (t2 + 3t + 1) -5/2

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

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Q: Find the derivative of the function f(x) = V(a3 + 7x) by using the definition %3D of the derivative.

A: Let's find.

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

A: We need to find the stationary value of f(x,y)=x3-6x2-8y2   For that first we need to find the value…

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. f(t) = 8t2/3 – 4t1/3 + f '(t)=

A:

Q: Calculate derivative f(a) = 13= 43 30 х %3D d 13 -30 x'3 t16e^)= %3D

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Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Consider the function f(x) = (x² – 6)(a² – 6æ) Compute the derivative. f'(x) =

A: In this we are going to use product rule of derivative to find out the solution so I'm providing…

Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

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Q: For function f (x, y) y? x2+1 Find the maximum rate of decrease of f at the point (1, 2)

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Q: Find the total a.f(x, y) = ex² + y² 2 derivative of t

A:

Q: Find the average rate of change of the function f(x) = x2-40x+28 over the interval [10, 50].

A: topic - average rate of change of function over interval

Q: Find the derivative of the function. f(t) = 4t2/3 - 8t/3 + 4 8.

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Q: Find the derivative of the function Z=3t^(11/3)-2t^(9/4)-t^(1/2)+1

A:

Q: Find the derivative of the function. h(t) = t2(2t + 3)3

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Q: Find the linearization for f(r) 10, and use it to approximate 12 near a=

A: We want to find the approximate value of 112 by linear approximation of the function ,fx=1x by…

Q: Find the derivative of the function. f(t) = 7t2/3 − 4t1/3 + 3

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Q: Differentiate the function y=xcosx  and y=(x+1)e2x.

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Q: y = V4x3 –6

A:

Q: Find the derivative of the function g(t) = ((2t - 1)2) / ((3t + 2)4 )

A: We will need quotient rule. So assume u and v:

Q: Differentiate the function. f(t) = 7 - 글

A: We have to differentiate of the  function

Q: find the second order derivatives of function f(X)  exsinxcos2

A: To find the second derivative of the below function. fx=exsinxcos2x

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

A: Topic:- derivatives

Q: Find the derivative of the function. f(x) = ex2 + 2 %3D f'(x)

A:

Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

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

A:

Q: Differentiate the function. y = In(12 + t – t31)

A: We have to find derivative

Q: Find the first and second derivatives of the function. g(t) = t²(6t + 3)* %3D

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Q: Differentiate the function t= (ln(y)) / y³

A:

Q: Consider the function f(x, y) = x² + xy - 5x- y+1. Then:

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Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

A:

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

A:

Q: Find the derivative of the function. t2 (a) F(æ) = |7 1+t3

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Q: Find the derivative F'(x) F(x) = (t? - 2t + 3)dt 1. -t2 +3t +c 3 О x2-2х +3 O x2 - 2x +5

A:

Q: Find the third derivative of f (z) = V12z+I. a |a| b f" (z)

A:

Q: Find the average rate of change of f(x) = 3x2 +2x – 2 on the interval [2, t].

A: 555

Q: The derivative of the function y = 2t 1 A V2t 1 2t/2t 1 2t/2t 1 D B.

A: Definition used -            Power rule of derivative -…

Q: Find the derivative of the function. f(x) = /7+ V5+ VI f '(x) = %3D

A:

Q: Differentiate the function P = 5t³ + 4e'. dP dt

A: GIVEN: P = 5t3 + 4et TO FIND: dPdt

Q: Find the derivative of the function. f(x) = /2+ V1+ VI %3D f '(x) %3D

A:

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: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

Q: Find the first and second derivatives of the function. g(t) = (3t2 - 3)2 (8r?) %3D

A:

Q: Find the average rate Of change of.. f(x)= x²-1xI [3,2] on

A: Given: fx=x2-x, x∈2,3 we know that average rater of change of a functionfx on interval a,b is given…