Under construction Stations under construction may not yet contain a good range of resources covering all the key questions and different types of problem.

When and how can we differentiate the product or quotient of two functions?

Key questions

  1. 1

    How does the area of a rectangle change when we vary the lengths of the sides?

  2. 2

    How can we differentiate the product of two functions?

  3. 3

    Do we need a rule for differentiating a quotient of functions?

  4. 4

    What do we mean by integration by parts, and when is it useful?

Loading resources...
No resources found.

Developing...

Resource type Title
Fluency exercise Integral chasing II

Review questions

Title Ref
Can we differentiate $e^{2x}( 2 \cos (3x) + 3 \sin (3x))$? R6530
Can we find all three integrals? R5126
Can we find the area between $y=e^{-x}$ and $y=e^{-x}\sin x$? R9312
Can we find the repeated root for $4x^4+x^2+3x+1=0$? R9082
Can we find this body's displacement from $O$ when its velocity is $0$? R8774
Can we show the function $(2x+1)/(x^2-1)$ can take all real values? R9329
Can we sketch $y=ax/(x^2+x+1)$ when $a$ is positive? R7129
Can we sketch $y=x^2/(1+x^4)$? R5501
Can we sketch the curve $y=(x-a)e^x/(x-b)$? R9898
Can we sketch the curve $y=1/((x-a)^2-1)$? R6855
Can we sketch the curve $y=e^{-x}/(1+x^2)$? R9484
Can we sketch the graph of $y=x(x+1)(x-2)^4$? R8387
Given that $y = (x+6)^7(x-9)^8$, can we find $dy/dx$? R9795
How could we integrate $e^{-x}\sin^n x$? R8134
If $dy/dx$ is inversely proportional to $x^2$, can we find $y$? R7410
If $y=(x^2+1)/(x^2-a^2)$, then $y$ cannot take which values? R8765
If the gradient is $x(1-x^2)e^{-x^2}$ can we find the stationary points? R6620
If this cubic has two equal roots, what can $p$ be? R5196
If we can sketch $y = f(x)$, can we sketch $y^2 = f(x)$? R6863
What is the average density of this spherical planet? R8152
When will the arclength $QR$ take a maximum value? R8936
Where are the stationary points on $\cot x-8\cos x$? R6549
Which is the greater of $e^{\pi}$ and $\pi^e$? R8671
Which values can $x(x-3)/(x-4)$ take? R9391