3 If f(x) = 2(x - 3)°, evaluate f'(2). 4 The curve y= Vx-3 has a tangent with gradient at point N. Find the coordinates of N. 5 For what values of x does the function f(x) 1 have f'(x) = 4x-1 49

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z= ;d'z/dx² 1+x2 2. Y (3x+2)* ;y" 3.…

A: 1) Given: Z=21+x2 Differentiating Z with respect to x, dZdx=2×ddx1+x2-1       =2×-11+x2-2×ddx1+x2…

Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

A:

Q: 3. Find the gradient of the function and the maximum value of the directional derivative at the…

A: As per our guidelines,we are supposed to answer only one asked question.So kindly repost other…

Q: dy 2,3 For the curve xʻy' + x = 2, implicit differentiation gives us dx

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

A:

Q: x tan(yz) ey – 4x3z2 3: Find the total derivative of f(x, y, z) =

A:

Q: Show that the given femction satisties G-R Q. 4. conditions at origin but doesnot have a derivative…

A: Given we have given a function  f(z) = (x3-y3)+i(x3+y3)x2+y2,    if z≠0              0            ,…

Q: 3) (a) Find the oirectional derivative of f(x, y) = xe-y x at (-2,1) in the direction u= i-j. O…

A: We need to find the directional derivative in the direction of vector u

Q: 3. find the derivative of the function at Po in the direction of u. f (x, y,z) = 3e* cos yz,…

A:

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: 5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r,…

A: The directional derivative is the rate at which the function changes at a point in the direction .…

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: 1.What is the derivative of f(x)=e8x+3?

A:

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: 5. Find the linear approximation (i.e. the tangent plane) of f(x, y) = Vx/y at the point (9, 4) and…

A: The Local Linear approximation of f at (x,y) using the partial derivative f at (x0,y0) is given by…

Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

Q: find the derivative of y with respect to x, t, or u,as appropriate.13. y = ln (t/2) 14. y = ln…

A: Given question is to find the derivative of the function , which can be solved by using the chain…

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

A:

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

A:

Q: 22. The gradient of the implicit function to the curve x2 + y? = 13 at the point (2, -3) is A B 2 2

A:

Q: Given y(x) = cos(2x² – 2x), calculate the value of x when y is a maximum and when y is a minimum…

A: Given y(x) = cos(2x2-2x)  first we find the critical points using equation y'(x) = 0 . At critical…

Q: Economists have considered the output y of a manufacturing process as a function of the size of the…

A: The output of a manufacturing process as a function of the size of the labor is given as follows.…

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

A:

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

A:

Q: 8. The temperature of the xy-plane is given by the function f(x, y) = x²y+e¬¤. (a) At the point…

A: The direction of maximum decrease of a scalar function f(x, y) is given by the negative of the…

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: What is the first derivative of y=tanh(0³+30)? A y'=3(0²+1)sech (0²+30) dy =3(0²+ 1)sech²(0²+ 30) B…

A:

Q: 7. Given (x, y)= x' + y² a) Find the derivative at P(1,1) in the direction of " = u,i +u ;j b) In…

A:

Q: nd the derivative of (z.x)= X+c Cos (27 X) Point (0,2,1) in the direction at of V=i-sj+k

A: Directional derivative is dot product of gradient and normalised vector.

Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

A:

Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

A:

Q: H.W: Use the chain rule to find the derivative of w=x² + y² with dw with x cost+ sin t, y= cost-sint…

A: If w is a function of x and y and x,y are functions of t then we get by Chain rule, dw/dt=…

Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

A:

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

A:

Q: 4) Find the total derivative of the function: a.f(x, y) = ex²+y² 1 c. T(l,g) = 2₁ 2TT. b. z = x siny…

A: Total derivative of a function f(x,y) is given by df=fx dx+fy dywhere fx=∂f∂xfy=∂f∂y

Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

A:

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

A:

Q: Can you help me with this problem step by step?

A: Given:

Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

A:

Q: 21: dz 22: Find the derivative of f(y,x) = xe?y + cos(3yx) at a point (1,0,7)in the direction of V =…

A:

Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

A:

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

A:

Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

A: Given: The function is fx,y,z=xy+xz+yz-lnz2+1-4. Calculation: Obtain thethe value of  fxx,y, fyx,y…

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

A:

Q: Find the derivative of f(x, y) = e- x ln(y² + 1) at the point R(4,0) in the direction of w = (2, 1).

A: NOTE: Refresh your page if you can't see any equations. . the given vector is find the unit vector

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.