Differentation Rules Flashcards
What is the shortcut for the Stokoe rule?
- Multiply the bracket by the derivative of the bracket and then the original power of the bracket. Then subtract one from the power of the bracket.
For Example:
y = (3x2+4)4
dy / dx = (4)(6x)(3x2+4)4-1
dy /dx = 24x(3x2+4)3
When is the product rule used?
- When you have two brackets multiplied together.
When is the Quotient rule used?
- When you have two expressions divided by each other, such as a fraction.
What check should be performed before using the product rule?
- Check to see if the brackets can be easily multiplied, we often over complicate simple questions.
What is the product rule?
- dy/dx = U (dv/dx) + V (du /dx)
- Let u = one bracket.
- Let v = the other bracket.
How is the Quotient rule used?
- Let u = numerator.
- Lev v = denominator.
- Differentiate each component separately.
- Substitute into the following equation:
dy / dx = V(du/dx) - U(dv/dx) / V 2
What does sin(x) differentiate to?
- cos(x)
What does cos(X) differentiate to?
- -sin(x)
What does tan(x) differentiate to?
- Sec2(x)
What does ex differentiate to?
- ex
What is the rule for differentiating ex?
- You multiply the expression by the derivative of the power:
Example:
y = e4x
dy/dx = 4e 4x
What is the derivative of ln(X)?
- 1/x
What is the rule for differentiating natural logs?
- You need to use the stokoe rule.
- Do 1 / expression, multiplied by the derivative of the expression.
- This gives the simplified method that dy/dx of a log is equal to the derivative / original expression.
Example:
y = ln(3x2-1)
dy / dx = 1/3x2-1 x 6x
dy / dx = 6x/3x2-1
How would one differentiate parametric equations?
- Differentiate each equation separately.
- Apply the chain rule.
Example:
y = 4t3
x = 8t2
dy/dt = 12t2
dx/dt = 16t
dy/dx = dy/dt x dt/dx
dy/dx = 12t2 x 1/16t
dy/dx = 12t2/6t
dy/dx = 2t
