Derivatives

Question 1

Find d/dx

Answer 1

nx^n-1

Question 2

Find tangent and normal lines

Answer 2

f(a)=y
f’(a)=m

Question 3

If f(x)= a constant or a number
f’(x)/derivative of x=…

Answer 3

f’(x)=0

Question 4

If f(x) = x^n
Ex. (x) = x^7

Answer 4

f’(x)= nx^n-1
f’(x)= 7x^6

Question 5

If f(x)= #*x^n
Ex. f(x)=10x^4

Answer 5

f’(x)= #nx^n-1
Ex. f’(x)=104x^3

Question 6

f(x)= sum/difference of two functions

Answer 6

f’(x)= sum/difference of their derivatives

Question 7

the product of two functions
f(x) = M(x) * N(x)

Answer 7

f’ (x) = M(x) * N’(x) + N(x) * M’(x)

Question 8

quotient of two functions
f(x) = M(x) / N(x)

Answer 8

f’ (x) = ( N(x) * M’(x) - M(x) * N’(x) )
all over / ( N(x))^2

Question 9

Higher Derivatives

Answer 9

1st. Normal dy/dx (5x^3+4x^2-10x+1)
2nd. Multiply #*n^n-1 (15x^2+8x-10)
3rd. Repeat 30x+8
4th. 30
If there is no x, the whole thing goes away
If there is 1 x, the x leaves

Question 10

Equation of the tangent

Answer 10

Pick a point
Find the slope with f(a-h)-f(a)/h with given function and x
plug into point slope form

Question 11

How do you tell if f(x) is continuous?

Answer 11

Usually continuous except in piecewise functions where x is plugged in and it doesn’t equal each other
And removeable discontinuities

Question 12

How do you tell if f(x) is differentiable?

Answer 12

The limit exists
It is continuous
Find the slope
Left and right go to different numbers or +∞/-∞

Question 13

How do you find the equation of a line tangent to a curve at a given point

Answer 13

Plug in x
Find the derivative
Plug in x to the derivative
Use point slope

Question 14

if you have a function that is a parabola, what is the graph of the derivative

Answer 14

a line

Question 15

√x=

Answer 15

x^1/2
1/2x^-1/2

Question 16

How do you find the derivatives of numbers with negative exponents

Answer 16

Multiply -nx^-n-1

Question 17

How do you find the equation of a perpendicular tangent

Answer 17

Find the derivative
Plug in x
-1/y

Question 18

How do you find points

Answer 18

Find the derivative
Solve for 0