Differentiation

Question 1

When differentiation and integrating with trig, what unit must we use?

Answer 1

Radians

Question 2

List each result of differentiating sin(X) 4 times

Answer 2

1) cos(X)
2) -sin(X)
3) -cos(X)
4) sin(X)

Question 3

List each result of integrating sin(X) 4 times

Answer 3

1) -cos(X)
2) -sin(X)
3) cos(X)
4) sin(X)

(Reversed order to differentiation)

Question 4

When differentiating with sin, cos and tan what happens to the coefficient of x

Answer 4

is repeated outside the function
e.g. sin(KX) -> Kcos(KX)

Question 5

what happens when you differentiate tan(KX)

Answer 5

Ksec²(KX)

Question 6

What is the result of differentiating ln(KX)

Answer 6

1/X

Question 7

why, for any coefficient of X, is the derivitive of ln(X) the same

Answer 7

Log Laws!
ln(KX) = ln(K) + ln(X)
when differentiating constants, they disappear (ln(K))

Question 8

How would you differentiate an exponential graph, where x acts as the exponent?

Answer 8

For equation y = baseˣ
dy/dx = ln(base) * baseˣ