Apply the formula: f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$
this equation is called differentiation equation. By using this equation, we can find derivatives of different functions. $\Delta$x is the small change in the variable x. f(x) is a function of x. f '(x) is derivative of f(x).
Find the derivative of 7x + 10?
Step 1 :If f(x) = 7x + 10 then f(x + $\Delta$ x) = 7(x + $\Delta$ x) + 10
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ 7(x + \Delta x) + 10 – (7x + 10)}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ 7x + 7 \Delta x + 10 – 7x - 10)}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{7 \Delta x }{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ 7
=> f'(x) = 7.
Answer :7.
Find the derivative of f(x) = x ?
Step 1 :If f(x) = x, then f(x + $\Delta$ x) = x + $\Delta$ x
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ x + \Delta x – x}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ \Delta x}{\Delta x}$
=> f'(x) = $\lim_{\Delta x \to 0}$ 1
=> 1.
Answer :1.
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