Answer to Question #268653 in Calculus for Jess

Question #268653

Differentiate the function 𝑓(𝑥) = 5𝑥 2 + 2 using the first principle

Expert's answer

f'(x)=\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}

=\lim\limits_{h\to 0}\dfrac{5(x+h)^2+2-(5x^2+2)}{h}

=\lim\limits_{h\to 0}\dfrac{5x^2+10xh+5h^2+2-5x^2-2}{h}

=\lim\limits_{h\to 0}(10x+5h)=10x+0=10x

f'(x)=(5x^2+2)' =10x

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