When would you use a partial derivative? When you only need to differentiate half of a function. O When you need the derivative of a function of more than one variable. O When you only take the derivative of either the numerator or denominator of a fraction, but not both.

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: Find the derivative of the function. u4 + 8Vu f(u) = 8.u10 +14. 4" – 24. 1u -9. uT - 4 e" + u2 F(u)

A: givenf(u)=8u10+14(4)u-24(π)u-9uπ-4eπ+u4+8uu2diffrentiate with respect to u we know d(xn)dx=nxn-1and…

Q: Find the derivative of the function. h(t) = (t + 3)2/3(3t2 − 5)3

A:

Q: Let N be the number of applicants to a university, p the charge for food and housing at the…

A: Given that the N be the number of applicants to a university, p the charge for food and housing at…

Q: xy2+5x2-3y2+45=0  (1,5)   Evaluate the derivative at the given function point.

A: We have to find derivative

Q: A graph of y = f(r) is shown. In the same coordinate system, sketch a graph of the derivative…

A: To draw the graph of the derivative of the function

Q: Q-1Find the derivatives of the functions 1- Y+In (xy) =1 2. Inxf 9.

A: Note:- Derivative of the product of two functions is ddx fx·gx  =f'x·gx+fx·g'x   Part (1):-  Given…

Q: 2х - 3 y = 3x +4 The derivative is y'

A: Please refer the attached image for complete solution.

Q: Зах + b Find the derivative of h(x) Assume a, b and c are | 5c constants. h'(x) = %3D

A: The objective is to find the derivative.

Q: Find the derivative of the function. f(e) = (3t + 18)2/3 2 f (e) = 3/3t + 18

A: Topic:- derivatives

Q: f(2o+h)-f(x0) h 7- What is the approximate derivative of f(x) = 5x³ + 4x² if we use forward…

A:

Q: Given y = (ax? + bx )e -bx where a and b are constants. Find derivative of y with respect to x. e-bx…

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Q: xy(dx-dy) = x²dy + y?dx; when x = 2, y = 0

A:

Q: y to find the derivatives of the following functions before we continue. a. F(x) = x³ + 2x2 + x b.…

A: a) F'(x) = 3x2 +4x +1  b) F'(x) = 3x2 +2x +1  c) F'(x) = 9x2+3

Q: II. Find the first, second and third derivative of the function s = 3(8t" – 7)"

A: s = 3(8t4-7)4

Q: Find the derivative of the function. h(s) = -2/752 + 9 h'(s) : %3D

A: Given query is to find derivative of the expression.

Q: (2+3t2 3x2 dx 1+ x3 6. Find the derivative of the function F(t) = 2-3t2

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Q: The derivative of f(x) = %3D 3. 5' attains its maximum value at r =

A:

Q: Q. 6. Consider f (x) = -* + 2x + 1. x3 3x2 3 Use derivatives to separate the regions where function…

A: If f′(x) > 0, then f is increasing on the interval,and if f′(x) < 0, then f is decreasing on…

Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: At what value of x does the function f(x)=x' -3r? -9x change from deceasing to increasing? 1 -1 Find…

A:

Q: x + Va x2 1. Find the derivative of the function f(x) = in two different ways. Once with the…

A: 1 Given function,                  f(x) = x+xx2Differentiate f(x) with respect to x, using quotient…

Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: Find the derivatives of y= s2-a2 / s2+a2

A:

Q: A) Find the domain and range (for TWO only) 1) y = V9 - V9x 2) y = V4 – x² 3) y= у 3 B/ Draw the…

A: given is 1) y=9-9x    y=9-3xdomain =x∈R : 0≤x≤9range ={y∈R : 0≤y≤3}

Q: Use the Chain Rule to find the derivative of the function. y = (x + Sx?)-1

A: Derivative of function

Q: 60.) f(x, t) = x²e¯¤¹; fm, fixx

A:

Q: Find the anti-derivative of g (x)=−8ex+4 − 5/ x+7. (Do not include the constant C in your answer.)

A: We have to find the antiderivative of g(x) .g(x) is given by:

Q: Let `h (x) = -3tan^5(-7x)` Determine the derivative of 'h`. (I 'h'(x)=' Determine the slope of `h`…

A: We have to find h'(x) and h'(7)

Q: Find the derivative of the function. (x² + 1)6*². 1 u(x) = u'(x) =

A: This question is related to differentiation solve in step 2.

Q: Find the derivative of the function.

A: the given function is: hs=s5+2s+6s13 we have to find the derivative of the given function.

Q: Evaluate the derivative of the function at the given point. 1 y%3D 4t + 9 .t%3D2 (Type an integer or…

A:

Q: Find the absolute extrema of the function f(x) = (x2 + 18)273 on the interval[-4,3]. Find the second…

A:

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

A: Here we have to find the derivative by using power rule and the properties of the derivative.

Q: What is the value of y' at x=-4 is ______? Evaluate the derivatives of the given function for the…

A: The function is given by y = 5x2-x+53-3x-x2 To evaluate : The value of y' at x =-4

Q: 음고+ 음 + 2V- e The first derivative of y = 3x5 is %3D

A: Recall: dxndx=nxn-1 dc1f(x)±c2g(x)dx=c1df(x)dx±c2d[g(x)]dx ; where c1 and c2 are constants.…

Q: 7x +5 5x +1 Evaluate the derivative of y = In where x = 3.25.

A:

Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

A:

Q: x² + 1 What is the derivative of y= - x2 + 4 A None of the given choices 10x B (x² + 4)²

A: The given function is y=x2+1x2+4 Differentiate with respect to x,

Q: State both forms of the Chain Rule for calculating the derivative of y = f(g(x)) with u=g(x). State…

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Q: Find the derivative of the function.

A:

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: Calculate the derivative of y = /x+ If the Chain Rule only needs to be used once, which functions…

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Q: 6. Find the second derivative of the function. f(P) = v1– 2P7 eC-2P

A: Some derivative formulas: ddx(fg)=fg'+gf'ddxfg=gf'-g'fg2ddx(a)=0ddx(xn)=nxn-1

Q: 4. Find the derivatives of the following functions. a. y= 2x b. y = x³ C. y= 4x -7

A: a. y=2x Differentiating both side with respect to x dydx=2b.y=x3Differentiating both side with…

Q: (b) Find the derivative of the function f(r) = ( + 6)1²(4 – 17.")18 X -

A: