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Differentiation pdf Name Level 2 Further Maths Differentiation Ensure you have Pencil or pen Guidance Read each question carefully before you begin answering it Check your answers seem right Always show your workings Revision for this topic www corbettmaths more further maths 1 7x2 dy Work out d x dy d x
V p qt 2 t 0 where p and q are positive constants and t is the time in seconds measured after a certain instant When t 1 the volume of a soap bubble is 9 cm 3 and at that instant its volume is decreasing at the rate of 6 cm 3 per second Determine the value of p and the value of q p 4 q 1
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You can write the derivative of p xeither as 1 2 p x or as 1 2 x 1 2 whichever you prefer Answer 2 Hint p xtanx This is a composition so ap ply the chain rule rst The outer function is p and the inner function is xtanx If you combine the chain rule with the derivative for the square root function you get p u 0 u0 2 p u
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In each of the three following cases find the general solution to the differential equation md2x dt2 cdx dt kx 0 sketch and describe the graph of a solution curve and explain why the case deserves the name it has Over damping c2 4mk 0 Critical damping c2 4mk 0 Under damping c2 4mk 0
Kuta Software Infinite Calculus Name Differentiation Rules with Tables Date Period For each problem you are given a table containing some values of differentiable functions f x g x and their derivatives Use the table data and the rules of differentiation to solve each problem
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V p qt 2 t 0 where p and q are positive constants and t is the time in seconds measured after a certain instant When t 1 the volume of a soap bubble is 9 cm 3 and at that instant its volume is decreasing at the rate of 6 cm 3 per second Determine the value of p and the value of q p 4 q 1
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Exercises H 124 005SS17 Derivative Worksheet Name The purpose of this worksheet is to provide an opportunity to practice di erentiation formulas for se tion 005 It will not be graded and you are not expected to nish in class There are commonly used formulas after the problems some of these problems might be challenging if you have
V p qt 2 t 0 where p and q are positive constants and t is the time in seconds measured after a certain instant When t 1 the volume of a soap bubble is 9 cm 3 and at that instant its volume is decreasing at the rate of 6 cm 3 per second Determine the value of p and the value of q p 4 q 1
Exercises H 124 005SS17 Derivative Worksheet Name The purpose of this worksheet is to provide an opportunity to practice di erentiation formulas for se tion 005 It will not be graded and you are not expected to nish in class There are commonly used formulas after the problems some of these problems might be challenging if you have
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