Calculus AB- Derivative Flashcards

d/dx [c]
The derivative of any constant is always 0

Derivative

d/dx [x^n]=nx^n-1

Power Rule

d/dx [f(x)]=f’(x)

Prime Notation

d/dx [1/x²]=d/dx[x^-2]

Derivative of a Rational Function

d/dx [√x]=1/(2√x)

Derivative of a Radical Function

d/dx [sin(x)]=cos(x) *x’

Derivative of Sine

d/dx [cos(x)]= -sin(x) *x’

Derivative of Cosine

d/dx[tan(x)]=sec²(x) *x’

Derivative of Tangent

d/dx[cot(x)]=-csc²(x) *x’

Derivative of Cotangent

d/dx[sec(x)]=sec(x)tan(x)*x’

Derivative of Secant

d/dx[csc(x)]=-csc(x)cot(x) *x’

Derivative of Cosecant

d/dx[ln(x)]=x’/x

Derivative of Natural Logs

d/dx[log_b(x)] = 1/(x ln(b)) * x’

Derivative of a Log Function

1.) Take the derivative of the equation

2.) Set the derivative equal to 0 (This will find the points of intersection for x)

3.) Solve for x

4.) Plug in the x value into the original function to find the y points

5.) Combine the x and y terms to find the point

How do you find the points on the graph with a horizontal tangent line?

Opposite [b]: 1

Adjacent [a]: sqrt(3)

Hypotenuse[c]:sqrt(2)
*These values are not squared*

30 Degree Triangle

Opposite [b]: 1

Adjacent [a]: 1

Hypotenuse[c]:sqrt(2)
*These values are not squared*

45 Degree Triangle

Opposite [b]: sqrt(3)

Adjacent [a]: 1

Hypotenuse[c]:sqrt(2)
*These values are not squared*

60 Degree Triangle