Week 6 - Differentiation Flashcards
What 2 qualities make a function differentiable?
It must be:
-Continuous (unbroken)
-Without corners
Power rule of Differentiation:
If y = x^n then….
dy/dx = nx^(n-1)
What is the derivative of any single constant?
0
When is the chain rule used?
When there is a smaller function inside a larger function that needs differentiating
What is the derivative of any term without a power? Such as 3x
Just the number: 3
What is the Chain Rule of derivatives?
Find the derivative of outside function, leaving the inside alone, then multiply this by the derivative of the inside function.
What is the derivative of Sin?
‘Cosign’
=COS
What is the derivative of COS?
-Sin
How do you re-write a root as a power?
N Square root x =
X^1/N
How could you remove the fraction from this equation?
2 / (x^4 + 2)^3
By pulling the denominator up and making the exponent negative:
2(x^4 + 2)^-3
How do you remove a negative fractional exponent?
a^(-m/n) =
(1/a)^(m/n)
What is the exponential rule of differentiation?
When finding dy/dx of e^u; the answer is:
e^u X derivative of U
