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Tags:DerivativeImplicit DifferentiationRelated RatesHow-To Calculus

Solving a Related Rates Word Problem About Liquid Filling a Sphere

Author: ShaNisaa RaSun
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Answer" to reveal the answer to the problem.

Exercises

\(226.195\frac{\text{in}^3}{\text{min}}\)

Interpretation: The liquid is flowing from the tap at a rate of \(226.195\) cubic inches per minute when the radius is \(3\) inches.

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MLC WIR 20B M151 week4 #6

MLC WIR 20B M151 week4 #6 thumbnail
Using the Chain Rule to find the pattern for a higher order derivative

MLC WIR 20B M151 week4 #7

MLC WIR 20B M151 week4 #7 thumbnail
Finding the derivatives of compositions of functions from their graphs

MLC WIR 20B M151 week5 #10

MLC WIR 20B M151 week5 #10 thumbnail
Finding the points on a parametric curve where the tangent line is horizontal or vertical

MLC WIR 20B M151 week5 #4ab

MLC WIR 20B M151 week5 #4ab thumbnail
Finding the derivative of a function containing an inverse trigonometric function

MLC WIR 20B M151 week5 #4cd

MLC WIR 20B M151 week5 #4cd thumbnail
Finding the derivative of a function containing an inverse trigonometric function

MLC WIR 20B M151 week5 #4ef

MLC WIR 20B M151 week5 #4ef thumbnail
Finding the derivative of a function containing a logarithmic function

MLC WIR 20B M151 week5 #4ghi

MLC WIR 20B M151 week5 #4ghi thumbnail
Finding the derivatives of functions containing logarithms

MLC WIR 20B M151 week5 #5

MLC WIR 20B M151 week5 #5 thumbnail
Finding the derivative of a function containing a logarithms

MLC WIR 20B M151 week5 #6

MLC WIR 20B M151 week5 #6 thumbnail
Finding the equation of a tangent line to a function containing a logarithm

MLC WIR 20B M151 week5 #7a

MLC WIR 20B M151 week5 #7a thumbnail
Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7b

MLC WIR 20B M151 week5 #7b thumbnail
Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7c

MLC WIR 20B M151 week5 #7c thumbnail
Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #9a

MLC WIR 20B M151 week5 #9a thumbnail
Finding the tangent line to a parametric curve
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