Derivative Calculator

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Derivative is the change in one quantity when there is a relative change in another given quantity. The method of solving a derivative for a function is called a Derivation. Derivative calculator is a tool that helps to derive a function in relative to the chosen variable till the tenth order.

Example 1: Find the derivative of f(x) = 2x

If f(x) is a function with variable x. f'(x) is the derivative of f(x).

f'(x) is calculated by f'(x) = lim_{(h--> 0)} [f(x+h) - f(x)] / h

f'(x) = lim_{(h--> 0)} [f(x+h) - f(x) ] / h

f'(x) = lim_{(h--> 0)} [2(x+h) - 2(x)] / h

f'(X) = lim_{(h--> 0)} [ (2x+2h) - (2x) ] / h

f'(x) = lim_{(h--> 0)} [ 2h / h ]

f'(x) = lim_(h-->0) [2]

f'(x) = 2

Example 2: Find the derivative of the function f(x) = x² + 5

Using the same formula, we get:

f'(x) = lim_{(h--> 0)} [f(x+h) - f(x)] / h

f'(x) = lim_{(h--> 0)} [ ( (x+h)² + 5) - ( (x)² + 5 ) ] / h

f'(x) = lim_{(h--> 0)} [ x² + 2xh + h²+ 5- x² – 5] / h

f'(x) = lim_{(h--> 0)} [2xh+ h²] / h

f'(x) = lim_(h-->0) [ h(2x+h) ] / h

f'(x) = lim_(h-->0) [ 2x+h ]

f'(x) = 2 x

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