A level Flashcards
When can you use the chain rule?
To differentiate a function of a function
If y = [f(x)]^n then
dy/dx = n[f(x)]^n-1.f’(x)
If y = f[g(x)] then
dy/dx = f’[g(x)]g’(x)
When can you use the product rule?
When 2 functions u(x) and v(x) are multiplied together
If y = uv
dy/dx = vu’ + uv’
When can you use the quotient rule?
When one function u(x) is divided by another function v(x), to form a rational function.
If y = u/v
dy/dx = (vu’ - uv’)/v^2
How do you differentiate 1) y=e^x and
2) y=e^f(x)
1) dy/dx = e^x
2) dy/dx = f’(x)e^f(x)
Differentiate
1) y = lnx
2) y = ln[f(x)]
1) dy/dx = 1/x
2) dy/dx = f’(x)/f(x)
Differentiate
y = sinx
dy/dx = cosx
Differentiate y = cosx
dy/dx = -sinx
Differentiate y = tanx
dy/dx = sec(^2)x
Differentiate y = cosecx
dy/dx = -cosecx.cotx
Differentiate y = secx
dy/dx = secx.tanx
Differentiate y = cotx
dy/dx = -cosec(^2)x
Explain dy/dx=dy/du.du/dx
Another form of chain rule where u is a function of u and u is a function of x
Another case of chain rule
dy/dx = 1/(dx/dy)
Integral of x^n
(x^n+1)/(n+1) + C
Integral of e^x
e^x + C
Integral of 1/x
lnx + C
Integral of sinx
-cosx + C
Integral of sec(^2)x
Tanx + C
Integral of cosecxcotx
-cosecx + C
Integral of cosec(^2)x
-cotx + C
Integral of secxtanx
secx + C
Integral of x^n
(x^n+1)/(n+1) + C
