Consider the function

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

y(x) = \left(2x^{3} - 5x + 4\right)\left(x^{2} + 3\right)

. Answer the following questions. (i) Identify the first differentiation rule that must be applied to find

\dfrac{dy}{dx}

and write its statement. (ii) Briefly justify, in one or two sentences, why this rule is appropriate for the given function. (iii) Without completing the entire derivative, write the expressions for the derivatives of each individual factor of

y(x)

Related theory

Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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