Question Type 3: Learning to apply chain rule on more complex composite function with possible multiple chains Exercises

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

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

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

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

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

Differentiate $f(x) = \bigl(\sin(3x+\cos x)\bigr)^2.$

Find $y'=\frac{d}{dx}\Bigl[\ln\bigl(\sqrt{5x+3}\bigr)\Bigr]$.

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

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

Differentiate $y = \sin\bigl(e^{3x}\bigr)$.

Differentiate $h(x) = \bigl(\tan(2x)\bigr)^5$.

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