Find the derivative of $$ f(x)=5 x^{2} $$, $$ f^{\prime}(x)=\square $$

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UpStudy AI · Accepted Answer

1. The function is given by  
   $$
   f(x) = 5x^2.
   $$

2. To find $$ f'(x) $$, we use the power rule for differentiation, which states that if  
   $$
   g(x) = x^n,
   $$
   then  
   $$
   g'(x) = nx^{n-1}.
   $$

3. Applying the power rule to $$ f(x) $$:  
   $$
   f'(x) = 5 \cdot \frac{d}{dx} (x^2) = 5 \cdot (2x) = 10x.
   $$

Thus, the derivative is  
$$
f'(x) = 10x.
$$
$$ f'(x) = 10x $$.

Find the derivative of \( f(x)=5 x^{2} \), \( f^{\prime}(x)=\square \)

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