Differentiate the function; f(x)=1/((5-2x^3)^2)
We know from the properties of basic indices that a-x=1/ax, so 1/((5-2x3)2=(5-2x3)-2 where in this case, a=5-2x3and x=2. Then the function is differentiable by the chain rule. As dy/dx=dy/duXdu/dx, we let u=5-2x3, and by the principles of differentiation, du/dx=-6x2. If f(x)=y=(5-2x3)-2, we have that y=u-2, hence dy/du=-2u-3. therefore by the chain rule, dy/dx=dy/duXdu/dx=-2u-3X-6x2=12x2u-3=12x2(5-2x3)-3=12x2/(5-2x3)3.
So when f(x)=1/(5-2x3)2, f'(x)=12x2/(5-2x3)3.
BK
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