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 $y'$ 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 $x$.