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287 Answered Questions for the topic Derivatives



If a cylinder tank holds 100,000 liters of water, which can be drained from the bottom of the tank in an hour, then Toricellis law gives the volume V of water r

If a cylinder tank holds 100,000 liters of water, which can be drained from the bottom of the tank in an hour, then Toricellis law gives the volume V of water remaining in the tank after T minutes... more
Derivatives Calculus


Find the derivative dy/dx

y=5uv4 (assume that u and v are dependent on the variable x)
Derivatives Calculus Functions


Find the derivative of the function (PLEASE HELP)

L(t) = -2.3 + 0.24t + 0.0027t^2   Question: Find dL/dt for 18 ≤ t ≤ 38, using the limit definition of the derivation and then using differentiation rules. 
Derivatives Calculus 1


Find the absolute extrema of the function on a closed interval

g(x) = 7 secx,  [-pi/6, pi/3], solving for minimum (x,y) and maximum (x,y).


Calc 1 Help! For a certain graph y=f(x) the tangent line at the point (2,f(2)) goes through the points (3,2) and (5,-4). Find f(2) and f'(2)

I am unsure of how to do this problem or even set it up. I didn't know whether to find the slope of the two points or not and was wondering if one of you all could help me. I would really... more



how do you do the derivative of this?


Is derivative of several variable function an vector quantity?

Please tell me that derivative of several variables function is vector or scalar?
Derivatives Math Differentiation


Derivatives - local extremes

f(x) = x3 - 8x2 + 5x   Compute algebraically the x-coordinates of the points on the graph of f where the tangent to this graph is horizontal.    I know how to find the derivative:   f′(x) =... more


Use the chain of rule to calculate dy/dx of y=(3x+5)^8

Please help me find the answer using the chain rule 
Derivatives Calculus Graphing


Derivatives effect on graph?

sketch the graph of the function x^4-x^3   i was wondering on how do we get the points that we have to plug on the graph? Are they only the x and y intercepts?



Calculate (y^(k))(0) for 0 is less than or equal to k which is less than or equal to 5, where y=5x^4+ax^3+bx^+cx+d (with a, b, c, d the constants)
Derivatives Calculus Optimization


Very confusing optimization question!

I am really confused about this equation and how do you derive the volume and area equation! ” An open-top rectangular box is to be 6 meters high and have a volume of 300 cubic meter. Find the... more



A man on the 12th floor of a building sees a bucket (dropped by a window washer) pass his window and notes that it hits the ground 1.3 s later. Assuming a floor is 12 ft high (and neglecting air... more



The atmospheric CO2 level A(t) at Mauna Loa, Hawaii at time t (in parts per million by volume) is recorded by the Scripps Institution of Oceanography. The values for the months January-December... more
Derivatives Calculus


Use logarithmic differentiation to find y’ : (question in description)

y=(5√x4)cosx ÷ 3(2x+6) simplify answer 
Derivatives Limits Logarithms


FInd the 1000th derivative of Ln(x+1)

I am struggling as i know the sequence but got no idea how to describe it mathematically!


If derivative doesn't exist at a point then this critical point cannot be a local minimum or maximum ? True or false?

I think the question is false. Knowing that a critical point MUST be a point where the derivative is 0 or undefined, then of it can be a local min/local max. Please correct me if im wrong
Derivatives Trigonometry Limits


Points of discountuity

how do we find pointa of discountity of trignometric functions such as tan^-1(5x)   or sec(5x)
Derivatives Calculus Pre Calculus


Derivative Equations

Let f(x)=x^3+3x^2-144x+1    on what interval is f increasing (including the endpoints in the the interval)? Interval of increasing = ----   On what interval is f decreasing (including the... more
Derivatives Calculus Pre Calculus


Derive this equation

Derive f(x) = 5+ (4/x) +(3/x^2)
Derivatives Calculus Pre Calculus


Derive the Equation

Let y=x^7-4x^5+8x^3-2x-7 Then y(2) is --- Then (dy)/(dx) is ---  (d(2))/(dx) is ---  The second derivative of y is ---  and y''(2) is -----
Derivatives Calculus Pre Calculus


find the derivative

find the derivative of: 10x^(1/4) + 7x^(-6)
Derivatives Calculus Pre Calculus


Derive the equation

If f(x) = 3/(x^2), find f'(1)
Derivatives Calculus Precalculus


Finding the Derivative

please show all work. Find the derivaI’ve of f(x)=2x^7


Let f(x)=5/(x-1), use definition of derivative then find equation of tangent line at x=2

Use the definition of the derivative((f(x+h)-f(x))/h) to compute dy/dx, then find the equation of tangent line at x=2. Step by step calculation
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