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# The Concept of 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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Derivative of polynomials and trigonometric functions [00:04:25]
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