Formulas Flashcards
Sec^2 x =
1 + tan^2 x
Cosec^2 x =
1 + cot^2
Sin2A =
2sinAcosA
Cos2A =
Cos^2A - Sin^2A = 1- 2Sin^2 A = 2Cos^2 A - 1
Differentiate e^x
3^x ln x
Differentiate e^kx
K * e^kx
Differentiate cos x
-sin x
Differentiate cos kx
- ksin kx
Differentiate cos^2 x
- use chain rule!! -2cosxsinx
1. Bring the power down 2(cosx) times by the differential of the bracket (-sinx)
Differentiate sin x
Cos x
Differentiate sin 2x
2cos 2x
Differentiate sin^2 x
*use chain rule!! 2sinxcosx
When differentiating parametrics what do x and y become
X is normal differentiation (1)
Y is differentiation x dy/dx so (dy/dx)
How to differentiate x^3y^2 with implicit differentiation
*use product rule!!
(3x^2 y^2 )+ (x^3 2y dy/dx )
How to do implicit differentiation
- Differentiate as d/dx
- Differentiate x normally, y as y’ dy/dx
- Get all the dy/dx on one side and factor them out
- Divide by the factor to just have dy/dx
How to integrate with parametrics
( | represents integration sign)
1. Write out |y dx
2. Differentiate x with respect to t (or wtv letter) and rearrange for an expression for dx
3. Substitute y and the expression for dx into integration
4. Should look something like | t^2 * 4t dt
5. Integrate with respect to t now
Area under the curve with parametrics
- Find expression for integration the same way
- If boundaries given in x, change to t
- If given in t LEAVE THEM
- Integrate with respect to t and substitute values for t in - like normal definite integrals in P2
Differentiate tan kx
Ksec^2 kx
