IB Mathematics Analysis and Approaches Question Type 2: Learning to Apply Chain Rule on Simple Composites Exercises

Differentiate $y=(4x^3-x{)}^3$ with respect to $x$.

Differentiate $y=(x^2+3x{)}^3$ with respect to $x$.

Differentiate $y=(x^2+5{)}^3$ with respect to $x$. [2 marks]

Find $y^{\prime }$ if $y=(2x^2+3x+1{)}^2$.

Find $\frac{dy}{dx}$ if $y=(x^5+x{)}^2$.

Find the derivative of $y=(x^2+1{)}^4$.

Find $\frac{d}{dx}(3x+2{)}^4$.

Differentiate $y=(x^3-4x{)}^5$ with respect to $x$.

Compute $\frac{d}{dx}\left((3x+1{)}^{\frac{1}{2}}\right)$.

Find $\frac{dy}{dx}$ for $y=(x^2-2x+3{)}^3$.

Differentiate $y=(5x-7{)}^{-2}$ with respect to $x$.

Differentiate $y=(2x+1{)}^{\frac{5}{2}}$ with respect to $x$.