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2. Use the definition of derivative to show that for the function

f(x)=3(x)^(1/3)

(f of x is equal to 3 x to the power 1/3)

we have f'(a)=a^(2/3), for every "a" belongs to "R" (Set of real numbers)

[Use the identity (a^3)-(b^3)= (a-b)((a^2)+ab+(b^2))]

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3. Differentiate the following and prove the necessary expressions as given

a) If y=xtanx

show that

x sin²x (dy/dx)=x²tan²x +y sin²x