Summary
Summary OCR MEI Mathematics: Year 2 Pure - Further Differentiation Cheat Sheet
- Course
- Institution
This document briefly summarises the key points in the Year 2 'Further Differentiation' topic of OCR's Mathematics (MEI) course.
[Show more]
1 review
By: tsmith3553 • 1 year ago
Seller
Follow
JodbyBerundi
Reviews received
Content preview
Further DifferentiationDifferentiating Exponential and Logarithmic Functions
dy
y = ex ⇒ dx = ex
dy
y = ekx ⇒ dx = kekx
dy
y = ax ⇒ dx = ax ln(a)
dy 1
y = ln(x) ⇒ dx = x
dy f ′ (x)
y = ln[ f (x) ] ⇒ dx = f (x)
Differentiating Trigonometric Functions
dy
y = sin x ⇒ dx = cos x
dy
y = sin kx ⇒ dx = kcos kx
dy
y = cos x ⇒ dx = − sin x
dy
y = cos kx ⇒ dx = − k sin kx
dy 2
y = tan x ⇒ dx = sec x
dy
y = tan kx ⇒ dx = ksec2 kx
Differentiating Functions of ‘y’ with Respect to ‘x’
● Sometimes you want to differentiate ‘y2’ or sin y instead of a function of x
● To do this, follow the golden rule:
u = f (y)
d du dy
dy f (y) = dy × dx
Example
d d dy
dx √y = dy (√y ) × dx
1 dy
= 2√y dx
Differentiating Implicit Functions
● Sometimes x and y are given as a jumbled equation rather than explicitly
saying x= or y=
● In this case, differentiate both sides with respect to x to find the derivative
● You can also apply the product rule to implicit functions
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller JodbyBerundi. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.89. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75632 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now