IB Mathematics Analysis and Approaches Question Type 3: Learning to Apply Chain Rule on More Complex Composite Function with Possible Multiple Chains Exercises

Differentiate $h(x)=\sin ((2x+1{)}^4)$. [3 marks]

Find the derivative of $y=\arctan \left(e^{3x^2}\right)$.

Find the derivative of $f(x)=\ln (3x^2+5)$.

Find the derivative of $f(x)=e^{e^{2x}}$. [3 marks]

Differentiate $$y=\ln ((3x+1{)}^2+e^{4x}).$$

Differentiate $$f(x)=(\sin (3x+\cos x){)}^2.$$

Find $y^{\prime }=\frac{d}{dx}\left[\ln \right(\sqrt{5x+3}\left)\right]$.

Compute the derivative of $y=\cos \left(e^{\ln (x)+x^2}\right)$.

Compute the derivative of $g(x)=e^{\sin (x^2)}$.

Differentiate $y=\sin \left(e^{3x}\right)$.

Differentiate $h(x)=(\tan (2x){)}^5$.

Find $f^{\prime }(x)$ for $f(x)=\ln (x^2+1)+\sin (e^{3x})$.