Letƒ (t) be the depth, in centimeters, of water in a tank at time t, in minutes. (a) What does the sign of f' (t) tell us? (b) What does f' (21) = 14 mean? (c) Using the information in part (b), at time 21 minutes, find the rate of change of depth, in meters, with respect to time in hours. Enter the exact answer. The rate of change of depth, in meters, with respect to time in hours is meters/hour.

Q: g(x) = %3D I+3 32C

A: Derivatives

Q: f(x) = cot-1 Vx – 1

A: Given, fx=cot-1x-1

Q: Let f(x) = x² – 4x + 4. (a) Find the derivative of f. (b) Find the point on the graph of f where the…

A: Given function is f(x)=x2-4x+4 then a) derivative of function is f'(x)=2x-4 Derivative of the…

Q: Question The derivative of the function y e(tanx-2 vx) 1s:

A:

Q: Find the second derivative of the function. f(x) = x cos(x) f"(x) =

A:

Q: Find the derivative of the function. x coS X y = e*cos x

A: Differentiation is the rate of change of some variable with respect to the other variable. Chain…

Q: Find the derivative of the function. (x) = e+2 + 3 f'(x) : II

A:

Q: Find the derivative of the function f(x y) =x2+ xy + y2 at the point (6, 7) in the direction in…

A:

Q: tind the first derivative of the fanction i2 () =メ ニフ(x-1)

A:

Q: 17 Find derivative : f(t)= SVE et +t. f'(t) = ? %3D

A:

Q: What is the millionth derivative of f(x) = e x ?

A: ex

Q: Find the derivative of the function g(x)= tanx/e^x.

A: This problem can be solved by the quotient rule in derivatives.

Q: Find the derivative of the function.

A:

Q: Calculate the first derivative of the function. Use the correct notation to label your answer. S(2)…

A: f(x)=x+x+xdifferentiate w.r.t xf'(x)=12x+x+x×(1+12x+x×(1+12x))

Q: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: R(x)= 1 dt . 76 +4 Use FTC part II to find the derivative of the function

A:

Q: Find, or approximate to two decimal places,the derivative of the function f(x) = ex sin x at the…

A: fx=ex sinx By using graphing utility, we get

Q: What is the derivative of y=e^x?

A: The derivative of a function y=f(x) gives the rate of change of that function with respect to x.…

Q: Find the average rate of change of f from 0 to π /6 . f(x)= tan x

A: Given :           f(x) = tan x   To find the average rate of change of f from 0 to π6.

Q: Vith its derivative. A. f(x) S'(x) D. B.

A:

Q: Find the derivative of the function f. f(x) = e¯X tan(4x) %3D f'(x) = %3D

A:

Q: What is the second derivative of f (x) = e²?

A:

Q: Question * The derivative of the function y = x(tan¬1(3x))² is:

A:

Q: What is the third derivative of f (x) = a + cosæ?

A:

Q: Find the derivative of the function. (x) = T + 5cos x %3D f (x) = %3D

A: solve the following

Q: 9) Find the derivative of each function a)f(x) = x'e* %3D

A:

Q: Of the two functions f and g in Figure , which is the derivative of the other? Justify your answer.

A: If the slope of a graph of a function is constant at a point, then the slope of the graph of its…

Q: Find the average rate of change of f from 0 to π /6 . f(x)= tan(2x)

A: Given: fx=tan2x To Find: The average rate of change of the given function from 0 to π6

Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: Evaluate the derivative of the function y = 2tan ",²+In (e +e).

A:

Q: Find the second derivative of the function.

A: Given,         f(θ)=3tanθ

Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

A:

Q: ind the derivative of the function defined by 1 e dt F(x) x2 1 int: You need to use the product rule…

A:

Q: Is there any difference between finding the derivative of f(x) at x=c and finding the slope of the…

A: Definition type problem

Q: nd the derivative of the function y = arctan x + 1+x2

A:

Q: (a) Use the definition of the derivative to calculate the first derivative f'(x) for the function…

A:

Q: et y = (xº + 4)*. + 4)*. se the General Power Rule to find the derivative.

A:

Q: What is the first-order derivative of y = x^y?

A:

Q: 9. Evaluate the derivative of the function y with respect to x. y = x**

A:

Q: Find the derivative. f (x) = e* COS X %3D

A:

Q: Find the derivative of the function. y = a° + cos (x) y'(x)

A:

Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

A:

Q: Find the derivative f(x) , f(x) = / sec (t) dt sec x -sec x tan x

A:

Q: What is the second derivative of * f(x) = e²?

A: We have to find second derivative of the function: fx=ex2 We know the formula of derivatives,…

Q: find the derivative of the function  F(x)= e^x/e^x + 8

A:

Q: Find the average rate of change of f from 0 to 9. f(x)%3D tan (3x)

A:

Q: (n2 – 1)* 31. H (r) = (2г + 1)8

A: In the question it is asked to calculate the derivative of H(r)=(r2-1)3(2r+1)5 using chain rule.

Q: Let "g" be the function given by "g(x) = lim as h approaches 0 of [sin (x+h) -sinx]/[h]". What is…

A: Given  g(x) = sinx Instantaneous rate of change  g'(x)=limh→0sinx+h-sinxh

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.