Question

Derivatives Find and simplify the derivative of the following

functions

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: Evaluate the limit In(t + 6) lim e"i + In(t + 6)j+ t – 7 Enter your answer in i, j, k form.

A: Use linear property of limit and use limit separately

Q: If a ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height in feet a...

A: Given that: A ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height ...

Q: 17/27 - 1/15

A: The given expression is, 1727-115 The LCM of 27 and 15 is 135

Q: Including 8% sales tax, an inn charges $162 per night. Find the inn’s nightly cost before the tax is...

A: Let the inn's nightly cost is $x. Including 8% sales tax on it the charge becomes $162.

Q: In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

A: We know that, the mid point x,y of a line segment having end points x1,y1 and x2,y2 is calculated as...

Q: Evaluate the function at the given values of the independent variable and simplify : f(x) = x/lxl , ...

A: Given that, f(x) = x/lxl Then we get, f(6) = 6/l6l f(6) = 6/6 f(6) = 1

Q: Determine the volume of the solid obtained by rotating the portion of the region bounded by y=2squar...

A: First we have to plot the given region.

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle be...

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has ...

Q: Find the domain of the function g(x) = (x - 6)/(x2 - 36).

A: We have to find the domain of the function g(x)=x-6x2-36.

Q: Evaluate the integral, if it exists. ∫01v2 Cos (v3) dv

A: Click to see the answer

Q: Sets in spherical coordinates Identify and sketch the followingset in spherical coordinates. {(ρ, φ,...

A: we have, {(ρ, φ, θ): ρ = 4 csc φ, 0 < φ < π/2} We know that, csc φ =ρρ2-z...

Q: Fill in the blank/s: The total amount of acid in x milliliters of a 9% acid solution and y millilite...

A: Click to see the answer

Q: Evaluate the integral. inegral 1 to 2 [(4 y2 -7y -12 )/ y (y+2)(y-3) ]dy

A: Given: ∫124y2-7y-12y(y+2)(y-3)dy To determine: We can solve us...

Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin x g(æ) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product...

Q: Use a calculator with a yx key or a Λ key to solve: The 1986 explosion at the Chernobyl nuclear powe...

A: Use a calculator with a yx key or a Λ key to solve: The 1986 explosion at the Chernobyl nuclear po...

Q: Solve the equation (2 cos x + √3)(2 sin x + 1) = 0 on the interval [0, 2π).

A: Click to see the answer

Q: Plot the given point (0, -3) in a rectangular coordinate system.

A: we have to plot the point (0,-3) in a rectangular coordinate system.

Q: Sole Hese of caustion. Jystens 25(-3x2+ 3y 2=0 24-3422 + 3 x 2 =D0 3 x y -x'-43 =0

A: We are given three equatrions - 2x-3x2z+3yz=0.....(1)2y-3y2z+3xz=0.....(2)3xy-x3-y3=0..........(3) (...

Q: Integration techniques Use the methods introduced evaluate the following integrals. ∫sec49 2z tan 2z...

A: The given integral is ∫sec49 2z tan 2z dz

Q: 3. If you ride the "Drop Zone" at Canada's Wonderland, you will fall toward the ground at speeds in ...

A: Given:

Q: If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2? Explain your reaso...

A: Given f(2) = 4 Then we get, we cannot precisely say that, "As x tends to 2, f(x) approaches zero."

Q: Use the rules of differentiation to find the derivative of the function f(t) = /6

A: Known fact: ddxkx=k.

Q: Determine the convergence or divergence of the series

A: Known fact: If limn→∞ an ≠0 then ∑n=1∞ an diverges.

Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane ...

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or (x,y,z)=0,0,2+t1,1,3+s2,0,-3⇒x=t+2s...

Q: Find the derivative of the function at Po in the direction of vector A h(x, y, z) = cos(xy) + e>% + ...

A: Click to see the answer

Q: The cylindrical water tank shown in the figure has a height of 18 feet. When the tank is full, a cir...

A: Given that the height of the cylindrical tank is 18 feet. After 30 minutes the depth of water is 12 ...

Q: Consider the function g(r) = arccos(In r). (a) Compute the domain and range of g(r). (b) Prove that ...

A: the given function is: gx=arccos(lnx) (a) we have to compute the domain and range of g(x). (b) we ha...

Q: Let g be defined on an interval A, and let c ∈ A. (a) Explain why g'(c) in Definition 5.2.1(Differen...

A: Given that function g is gefined on interval A and c∈A

Q: Suppose you find the linear approximation to a differentiablefunction at a local maximum of that fun...

A: It is known that the linear approximation of a differentiablefunction at a local maximum of that fun...

Q: The half-life of cesium-137 is 30 years. Suppose we have a100-mg sample.(a) Find the mass that remai...

A: Given that the half-life of cesium-137 is 30 years. (a) Substitute y=50, t= 30 and y(0)=100 in yt=y0...

Q: Find r′(t), r(t0), and r′(t0) for the given value of t0 = /2. Then sketch the curve represented by t...

A: r( t ) = 3 sin t i→+ 4 cos t j→r( t0 ) = 3 si...

Q: Evaluate the limit In(t + 2) 6 lim t – 6 t 2 t+0 Enter your answer in i, j, k form.

A: Click to see the answer

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the definit...

A: Given function is fx,y=x2+y2. ∆z=fx+∆x,y+∆y-fx,y=x+∆x2-y+∆y2-x2-y2=x2+∆x2+2x∆x+y2+∆y2+2y∆y-x2-y2=∆x2...

Q: Calculate the area enclosed by y=sin x, y=cos x and x/pie for each of the following intervals: a) ...

A: our objective is to find the area under the curve

Q: Please help me

A: Solve x−2ydx+ydy=0

Q: Find all solutions to the equation (x2 − 5x + 4) · ln(x − 2) = 0.

A: Given, The equation (x2 − 5x + 4) ln(x − 2) = 0 We have to find the all the solution of the equ...

Q: The rate of change of annual U.S. factory sales (in billions of dollars per year) of a certain class...

A: Change of rate in sales per year S(t)=0.12t2-1.01t+5.7 billionsyearsales every year is given bysal...

Q: 3) f(x) = e on which find the mterval(s) f(x) (if any) is increasing

A: Use the necessary condition for increasing function

Q: Draw a graph with 5 vertices and 8 edges. How can you prove that it is a simple graph or multi edges...

A: The wheel graph has 5 vertices and 8 edges. The required graph is shown below.

Q: Sketch the graph of the equation x + 2y + 6 = 0

A: Sketch the graph of the equation x + 2y + 6 = 0

Q: An object is traveling around a circle with a radius of 10 m. If in 50 seconds a central angle of 1/...

A: Click to see the answer

Q: 38. I| x²ydA, R=[-1,1] × [0, 2]

A: Given: ∫∫Rx2ydA , R=-1,1×0,2

Q: Use the inequality in (2) to approximate (-1)*+1 n! n=1 to four decimal places.

A: Click to see the answer

Q: Find area of the region enclosed by the parabolasy = 4x – x² and y = x2 - 4x. %3D ation of the eu 13...

A: Click to see the answer

Q: Find the length S and area A

A: Given, Length of arc = s Area of sector = A Angle at center of circle = 40° Radius of circle = 11...

Q: 10 – x – x2 if x 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f...

A: Given that fx=10-x-x2if x≤42x-5ifx>4 (1) Find limx→4-fx Left hand limit: For x<4 , fx=10-x-x...

Q: For the following parametric equation x(t) = tan t and y(t) = sect find the %3! %3D d²y angent line ...

A: Explanation of the solution is given below...

Q: Find the following limit. lim t-3 - 5t² – 4t – 1, t2 + 6t – 27 , 4 · 4. cos(t) > < t – 3

A: Click to see the answer

Q: Find the area below the x-axis and bounded by the curve y=1-2x for 5<=x<=7.

A: The given curve is: y = 1 - 2x; where 5 <= x <= 7 The graph is as follows:

Q: Angle in two ways Find the angle between ⟨2, 0, -2⟩ and ⟨2, 2, 0⟩ using (a) the dot product and (b) ...

A: Given vectors are 2,0,-2 and 2,2,0. Let given vectors be A→ & B→ and angle between them be θ. Gi...

Transcribed Image Text

4/3 52. g(x)