432 Answered Questions for the topic Derivative
Use Logarithmic Differentiation to find the derivative of f(x)=(sin(2x))^4x
any help would be amazing
10/18/21
Find the rate of change of the angle of elevation dθdx when x=272 feet
A building that is 225 feet tall casts a shadow of various lengths as the day goes by. An angle of elevation (Theta) is formed by lines from the top and bottom of the building to the tip of the...
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10/18/21
Find the derivative of y=f(g(sin(x))) evaluated at x=0
use the following table to answer the question Function | f(x) | f'(x) | g(x) | g'(x) |x=0 | 2 | 5 | 0 | 2 |x=1 | 1 | -2 | 3 | 0 |x=2 | 4 |...
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Let f ( x ) = 3x^6 ln x , find f'(x), find f'(e^2)
Let f(x)=3x6 ln xf'(x)= 18x ln5 (x)+3x5f'(e2) = _____?This last part of the question is really confusing me, I know that you would typically enter the value of f'(#) into the equation, but what do...
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(chain rule) Let F ( x ) = f ( f ( x ) ) and G ( x ) = ( F ( x ) ) 2 . You also know that f ( 6 ) = 11 , f ( 11 ) = 3 , f ' ( 11 ) | = 7 , f ' ( 6 ) = 4
Let F(x)=f(f(x)) and G(x)=(F(x))2 .You also know that f(6)=11,f(11)=3,f'(11)=7,f'(6)=4Find F'(6)=____ and G'(6)= _____
Derivative Calculus
10/06/21
The current population of a certain bacteria is 2373 organism. It is believed that bacteria's population is tripling every 10 minutes. Approximate the population of the bacteria 6 minutes from now
The current population of a certain bacteria is 2373 organism. It is believed that bacteria's population is tripling every 10 minutes. Approximate the population of the bacteria 6 minutes from now
Derivative Calculus
10/06/21
The current population of a small town is 5062 people. It is believed that town's population is tripling every 11 years. Approximate the population of the town 7 years from now.
The current population of a small town is 5062 people. It is believed that town's population is tripling every 11 years. Approximate the population of the town 7 years from now.
10/06/21
Use algebra to evaluate the limit. lim h->0 ((4/(1+h)^2)-4)/h
We're supposed to use (f(x+h)-f(x))/h but I'm totally lost
10/05/21
Find the slope of the tangent line to the function f(x)=1/x−3 at a=−1.
any help would be greatly appreciated
10/05/21
Use the definition of the derivative to find the f′(x) for f(x)=x+1/x
Note: Using the definition means doing a limit and algebraically solving the limit. If you use the rules from the next section to do this derivative you will receive NO CREDIT.he states this under...
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10/05/21
Find the rate at which the spring is oscillating at t = 9 s. Round your answer to four decimal places.
A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t)=2cos t where s is measured in centimeters and t is measured in seconds. Find the rate at which the...
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Derivative Question
Need help going through this questions please. For the equation given below, evaluate dx/dy at the point (1,1).(3x - y)^4 + 3y^3 = 19dy/dx at (1,1) =
derivatives of a function
find the derivative of f(x)= (x^2 -sqrt(x))*3xim pretty sure you use the product rule of derivatives, but I cant seem to get the right answer.
tangent line equations
The line y = b + mx is tangent to the graph of f at x = 7. Given that f( 7) = 5, the derivative f'( 7) = 4, and f"( 7) = 4, find m and b.
09/20/21
Calculus Problem, object on rope
An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle t with the plane, then the magnitude of the force is F...
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09/20/21
Trigonometric Derivative as a Difference Quotient
I understand that the 2x might be treated as h. However, I don't know how to deal with cotangent.Limit (as h -> 0) of [8 * cot3(2x + pi/3) - 8 * cot3(pi/3)]/h
09/20/21
Calculus Problem Question, Elastic band
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically.The equation of motion is s(t) =...
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tangent line equations
find the equation of the tangent line to the function f(x)= 5/ (x^2) at the point (1,5). I tried finding the derivative to get the slope and then using y=mx+b to solve from there but I still am...
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Calc Limit question
Kind of stuck on this question, if someone could help I would greatly appreciate it!(1) The limit lim cos(x)-1/ x-4πx→4π represents the derivative of some function f(x) at some number . Find...
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09/10/21
Draw the direction field for the following differential equation and draw several solution curves.
I have been able to complete A, B, D, and E. I am struggling to finish C. I thought it was -1 but it is not. Draw the direction field for the following differential equation and draw several...
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Derivative Calculus
08/19/21
differential change
Let y=tan(3x+7).Find the differential dy when x=3 and dx=0.1 Find the differential dy when x=3 and dx=0.2
equations and derivatives
A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30...
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calcuating time and distance
Shannon is a lifeguard and spots a drowning child 30 meters along the shore and 40 meters from the shore to the child. Shannon runs along the shore for a while and then jumps into the water and...
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veolocity calculation
A stone is dropped from the edge of a roof, and hits the ground with a velocity of -180 feet per second. How high (in feet) is the roof?Note: the acceleration of an object due to earth's gravity...
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