ISC (Arts) Class 11CISCE
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Derivative - Derivative of Polynomials and Trigonometric Functions

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theorem

Theorem : Let f(x) = `a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0`  be a polynomial function, where `a_is`  are all real numbers and an ≠ 0. Then, the derivative function is given by
`(df(x))/(dx)` = `na_nx^(n-1) a_(n-1)x^(x-2) + ... + 2a_2x + a_1`.

Derivative of trignometric function

1. `d/(dx)` sin x = cos x 

2. `d/(dx)` cos x = - sin x

3.  `d/(dx)` tan x = `sec ^2 x `

4. `d/(dx)` sec x = sec x tan x 

5. `d/(dx)`  cosec x = - cosec x cot x

6. `d/(dx)`  cot x =` - cosec^2 x`

7. `d/(dx)`  log x = `1/ x`

8. `d/(dx)` constant = 0

9. `d/(dx) x^n = n x ^(n - 1)`

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