For a certain type of fish, the weight y,in grams,is related to the length in cm , by y=f(x)=0.007x^3 (a) Find f'(x) Xf'(x)= square

To find the derivative of the function \( f(x) = 0.007x^3 \), we will use the power rule for differentiation. The power rule states that if \( f(x) = ax^n \), then \( f'(x) = anx^{n-1} \).<br /><br />Given:<br />\[ f(x) = 0.007x^3 \]<br /><br />We apply the power rule:<br />\[ f'(x) = 0.007 \cdot 3x^{3-1} \]<br />\[ f'(x) = 0.021x^2 \]<br /><br />So, the derivative \( f'(x) \) is:<br />\[ f'(x) = 0.021x^2 \]<br /><br />Therefore,<br />\[ f'(x) = 0.021x^2 \]