432 Answered Questions for the topic Derivative

Derivative Calculus Logarithm

10/19/21

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... more
Derivative Calculus Trigonometry

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 |... more
Derivative Math Calculus

10/13/21

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... more
Derivative Math Calculus

10/11/21

(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

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... more
Derivative Math Trigonometry

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... more
Derivative Math Calculus

09/30/21

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) =
Derivative Math Calculus

09/28/21

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.
Derivative Math Calculus Tangent

09/23/21

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... more

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
Derivative Calculus Ap Calculus

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) =... more
Derivative Calculus Calc

09/12/21

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... more
Derivative Math Calculus

09/11/21

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... more

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... more
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
Derivative Calculus Algebra

08/19/21

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... more
Derivative Calculus Functions

08/15/21

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... more
Derivative Calculus

08/15/21

derivatives function

Find dx/dt at x=1 if y=3x^2−1 and dy/dt=4.
Derivative Math Calculus

08/15/21

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... more

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