Product Rule & Integration by Parts

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Resource type	Title
Building blocks	Producing a rule
Scaffolded task	How does your rectangle grow?

Resource type	Title
Fluency exercise	Integral chasing II
Many ways problem	Constant consistency

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

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