Topic 7- Differentiation Flashcards
What is the chain rule
f(x)^n becomes nf(x)^n-1 x f ’(x)
When is the product rule used
When a function is two functions multiplied
What is the product rule
If y=uv it becomes uv’+vu’
When is the quotient rule used
When a function is divided by another function
What is the quotient rule
If y=u/v it becomes (vu’-uv’)/v^2
What is the rule for parametric differentiation and explain
dy/dx = dy/dt / dx/dt (copy change flip then dt’s cancel out)
What is the order for differentiating trig
sin(x)»cos(x)»-sin(x)»-cos(x)
sin f(x) differentiates to
f’(x) cos f(x)
e^f(x) differentiates to
f’(x) e^f(x)
ln f(x) differentiates to
f’(x)/f(x)
a^f(x) differentiates to
f’(x) a^f(x) ln(a)
tan(kx) differentiates to
ksec^2(kx)
sec(kx) differentiates to
ksec(kx) tan(kx)
cot(kx) differentiates to
kcosec^2(kx)
cosec(kx) differentiates to
-kcosec(kx) cot(kx)
