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swati shrivastav Grade: 12
        

WHAT R THE GENERAL RULES OF DERIVATIVES, PLESE GIVE ME GENERAL IDEA ABOUT EACH OF THEM.


 


THANKS..

8 years ago

Answers : (1)

anjali SHARMA
8 Points
										












The general rules are as follows:


The Constant Rule

The derivative of a constant function is 0. That is, if c is a real number, then d/dx[c] = 0.



The Sum and Difference Rules

The sum(or difference) of two differentiable functions is differentiable and is the sum(or difference) of their derivatives.


d/dx[f(x) + g(x)] = f'(x) + g'(x)


 


d/dx[f(x) - g(x)] = f'(x) - g'(x)






The Constant Multiple Rule

If f is a differentiable function and c is a real number, then cf is also differentiable and d/dx[cf(x)] = cf'(x)



The Power Rule

If n is a rational number, then the function f(x) = xn is differentiable and d/dx[xn] = nxn-1



The Product Rule

The product of two differentiable functions, f and g, is itself differentiable. Moreover, the derivative of fg is the first function times the derivative of the second, plus the second function times the derivative of the first.


d/dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)






The Quotient Rule

The quotient f/g, of two differentiable functions, f and g, is itself differentiable at all values of x for which g(x) does not = 0. Moreover, the derivative of f/g is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator divided by the square of the denominator.


d/dx[ f(x)/g(x) ] = (g(x)f'(x) - f(x)g'(x)) / [g(x)]2      g(x) does not = 0






The Chain Rule

If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f(g(x)) is a differentiable function of x and d/dx[f(g(x))] = f'(g(x))g'(x)



The General Power Rule

If y = [u(x)]n, where u is a differentiable function of x and n is a rational number, then d/dx = [un] = nun-1u'.


 

8 years ago
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