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d/dx(1/x^{2} ) = 2 (x ^{21}) = 2* (x^{3}) = 2/x^{3}
f'(100) = lim_{(}_{h→0)} [f(100+h)  f(100)]/h
= lim_{(}_{h→0)} [99(100+h)  99(100)]/h
= lim_{(}_{h→0)} [9900 + 99h  9900]/h
= lim_{(}_{h→0)} 99h/h
= lim_{(}_{h→0)} 99
= 99
We’ll first need to divide the function out and simplify before we take the derivative. Here is the rewritten function.
The derivative is,
Derivative of sum of two functions is _____ of the derivatives of the functions.
In calculus, the sum rule in differentiation is a method of finding the derivative of a function that is the sum of two other functions for which derivatives exist. This is a part of the linearity of differentiation.
The derivative of the constant function f(x) = a for a fixed real number ‘a’ is:
Let f(x) = a, where a is a fixed real number.
So, f(x+h) = a
So, d/dx(f(x)) = lim_{(}_{h→0)}f[(x+h)−f(x)]/h
= lim_{(}_{h→0)} (a−a)/h
= 0
Hence, d/dx(a) = 0 , where a is a fixed real number.
Derivative of sum of two functions is sum of the derivatives of the functions. If , f and g be two functions such that their derivatives are defined in ______.
Derivative of quotient of two functions f(x) and g(x); g(x) ≠ 0 is given by is given by
This is a formula of question.
If f is a real valued function and c is a point in its domain, then is ;
This is a formula for finding derivative or differentiation which is represented by
but here at the place of x , c is written So this is equal to f'(c)
The derivative at x = 2/3 of the function f(x) = 3x is:
f(x) = 3x
f’(x) = lim(h→0) [f(x+h)  f(x)]/h
= f(x+h) = 3(x+h)
f’(x) = = lim(h→0) [3(x+h)  3(x)]/h
Putting x = ⅔
f’(⅔) = lim(h→0) [3(⅔+h)  3(⅔)]/h
= lim(h→0) [(6+3h)6]/h
=lim(h→0) 3h/h
lim(h→0) 3
The derivative of the function f’(⅔) = 3
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