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tell me formulas of differentiation

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tell me formulas of differentiation

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Solution

Sure, here are some basic formulas of differentiation:

  1. Power Rule: If f(x) = x^n, then the derivative is f'(x) = n*x^(n-1)

  2. Constant Rule: If f(x) = c, where c is a constant, then the derivative is f'(x) = 0

  3. Sum/Difference Rule: If f(x) = g(x) ± h(x), then the derivative is f'(x) = g'(x) ± h'(x)

  4. Product Rule: If f(x) = g(x) * h(x), then the derivative is f'(x) = g'(x)*h(x) + g(x)*h'(x)

  5. Quotient Rule: If f(x) = g(x) / h(x), then the derivative is f'(x) = (g'(x)*h(x) - g(x)*h'(x)) / (h(x))^2

  6. Chain Rule: If f(x) = g(h(x)), then the derivative is f'(x) = g'(h(x)) * h'(x)

  7. Derivative of e^x: The derivative of e^x with respect to x is e^x.

  8. Derivative of ln(x): The derivative of ln(x) with respect to x is 1/x.

  9. Trigonometric functions: The derivative of sin(x) is cos(x), the derivative of cos(x) is -sin(x), the derivative of tan(x) is sec^2(x), etc.

Remember, these are just the basic rules. There are many more rules and formulas in differentiation, especially when dealing with more complex functions.

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