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1. First Derivative example ( Enter your problem )
  1. Formula
  2. Examples
Other related methods
  1. First Derivative
  2. Second Derivative
  3. Third Derivative
  4. Fourth Derivative
  5. nth Derivative / Higher order Derivative
  6. Derivative at a Point
  7. First derivative test for Local maxima and minima
  8. Second derivative test for Local maxima and minima
  9. Critical Points and Extrema
  10. Increasing and decreasing functions at point
  11. Increasing and decreasing intervals

1. Formula
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2. Second Derivative
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2. Examples





1. `y=2x^3-2x^2-5x+4`
Find First Derivative


Solution:
`d/(dx)(2x^3-2x^2-5x+4)`

`=d/(dx)(2x^3)-d/(dx)(2x^2)-d/(dx)(5x)+d/(dx)(4)`

`=6x^2-4x-5+0`

`=6x^2-4x-5`
2. `y=log(x)e^x`
Find First Derivative


Solution:
`d/(dx)(log(x)e^(x))`

`=(d/(dx)(log(x)))e^(x)+log(x)(d/(dx)(e^(x)))`

`=(1/x)e^(x)+log(x)(e^(x))`

`=(e^(x))/x+log(x)e^(x)`

`=e^(x)(1/x+log(x))`

`=(e^(x)(1+log(x)x))/x`
3. `y=3cos(sin(x))`
Find First Derivative


Solution:
`d/(dx)(3cos(sin(x)))`

`=-3sin(sin(x))d/(dx)(sin(x))`

`=-3sin(sin(x))cos(x)`
4. `y=x^2sin(x)`
Find First Derivative


Solution:
`d/(dx)(x^2sin(x))`

`=(d/(dx)(x^2))sin(x)+x^2(d/(dx)(sin(x)))`

`=(2x)sin(x)+x^2(cos(x))`

`=2xsin(x)+x^2cos(x)`




This material is intended as a summary. Use your textbook for detail explanation.
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