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Michelle Arroyo

Answered question

2021-12-04

Find the derivatives of the following function f(x) from the first principles

x^{3}

Answer & Explanation

Oung1985

Beginner2021-12-05Added 16 answers

Step 1
Given

x^{3}

Step 2 Finding the derivatives of the following function
Let

f (x) = x^{3}

f^{'} (x) = L t_{x \Rightarrow 0} \frac{f (x + h) - f (x)}{h}

= L t_{x \Rightarrow 0} \frac{{(x + h)}^{3} - x^{3}}{h}

= L t_{x \Rightarrow 0} \frac{x^{3} + h^{3} + 3 x^{2} h + 3 x h^{2} - x^{3}}{h}

= L t_{x \Rightarrow 0} \frac{h (h^{2} + 3 x^{2} + 3 h x)}{h}

= 0 + 3 x^{2} + 0 = 3 x^{2}

=∴ f^{'} (x) = 3 x^{2}

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