Question

derivative of x^10 by first principle​

Answer 1

10ddx this is the answer

Answer 2

Answer:

The derivative of x¹⁰ = 10x⁹

Step-by-step explanation:

We have,

$\rm f(x) = x^{10}$

From the definition of first principle,

$\rm f'(x) = \lim\limits_{h\to0}\dfrac{f(x+h) - f(x)}{h}$

$\implies\rm f'(x) = \lim\limits_{h\to0}\dfrac{(x+h)^{10} - x^{10}}{h}$

$\implies\rm f'(x) = \lim\limits_{h\to 0}\dfrac{(x+h)^{10} - (x)^{10}}{(x+h) - (x)}$

$\implies\rm f'(x) = \lim\limits_{x+h\to x}\dfrac{(x+h)^{10} - (x)^{10}}{(x+h) - (x)}$

As we know that,

$\boxed{\sf\lim\limits_{x\to a} \dfrac{x^n - a^n}{x - a} = n\cdot(a)^{n-1}}$

By using this formula we get,

$\implies \rm f'(x) = 10\cdot{x}^{10-1}$

$\implies \rm f'(x) = 10\cdot {x}^{9}$

Hence the derivative of x¹⁰ = 10x⁹.