Further Differentiation (Chapter 5) Flashcards
1
Q
What is chain rule?
A
dy/dx= dy/du* du/dx
2
Q
What is product rule?
A
dy/dx= u’v+v’u
3
Q
What is quotient rule?
A
dy= u’v-v’u/v^2
dx
4
Q
What is the average rate of change
A
the gradient
y2-y1/x2-x1
5
Q
What is the instantaneous rate of change?
A
the derivative dy
dx
6
Q
derive y=e^x
A
y’= e^x
7
Q
derive y=e^f(x)
A
y’=f’(x)e^f(x)
8
Q
derive y=a^x
A
y’= a^x*ln(a)
9
Q
derive y=a^f(x)
A
y’= (ln(a))f’(x)a^f(x)
10
Q
derive y=ln(x)
A
y’= f’(x)/f(x)
11
Q
derive y=logaX
A
y’=1/x*lna
12
Q
derive y=sinf(x)
A
y’= f’(x)cosf(x)
13
Q
derive y=cosf(x)
A
y’= -f’(x)sinf(x)
14
Q
derive y=tanf(x)
A
y’=f’(x)*sec^2f(x)
15
Q
differentiating f(x)=> f’(x) gives the ___ derivative
hint: first or second
A
first
16
Q
differentiating f’(x)=> f’‘(x) gives the ___ derivative
hint: first or second
A
second
