differentiation

Question 1

equation to differentiate

Answer 1

dy/dx=nx^n-1

Question 2

what is the numerator and denominator letter based off

Answer 2

numerator: d(the letter you are looking for)
denominator: D(the letters in the equation)

eg. velocity (v) –> dv/dt= 3t²-4

Question 3

equation to differentiate 2 functions

Answer 3

f’g+fg’ (product rule)

Question 4

what is the quotient rule

Answer 4

(f’g- fg’)/g^2

f function is numerator, g function is denominator

Question 5

when is the quotient rule used

Answer 5

when dividing functions eg. y =cos x/x²

Question 6

steps to find the tangent and normal line ( 5 steps)

Answer 6

1) find gradient (through differentiation)
2) substitute given x value into new function (f(x)) to find m
3) substitute y, x and m value into y=mx+c to find c value
(this is the tangent equation)
4) the normal is perpendicular to the tangent so find a gradient that multiplies with tangent gradient to equal -1
5) find normal equation through substitution

Question 7

what is a stationary point

Answer 7

a point where the gradient is 0

Question 8

how to find minimum and maximum points

Answer 8

1) differentiate given function, make it equal 0
2) solve answer for 2 values for X, the negative x value is the max, the positive value is the minimum
3) substitute both values into the original equation for Y value
4) combine X and Y values for the points, the