Question Type 4: Learning to apply product rule on functions of x that are in multiple Exercises

Differentiate $y = (2x+1)\,(\ln x)\,\cos(3x)$ with respect to $x$ (for $x>0$). [5 marks]

Differentiate $y = e^x\,(\ln x)\,\cos x$ with respect to $x$ (for $x>0$).

Differentiate $y = x^3\,(\ln x)\,\cos x$ with respect to $x$ (for $x>0$).

Differentiate $f(x) = x^2\,e^x\,\sin x$ with respect to $x$. [4 marks]

Differentiate $y = x^2\,\sqrt{x}\,\ln x$ with respect to $x$ (for $x>0$).

Differentiate $y = x\,(\ln x)\,\ln(2x)$ with respect to $x$ (for $x>0$).

Differentiate $y = 3\ln x\,\sin x\,\cos x$ with respect to $x$ (for $x>0$).

Differentiate $y = x^3 \cos^2 x$ with respect to $x$.

Differentiate $y = (\ln x)^2\,\sin x\,\cos x$ with respect to $x$ (for $x>0$).

Differentiate $y = (\ln x)\,(x\sin x)$ with respect to $x$ (for $x>0$).

Differentiate $y = x^2\,e^{2x}\,\ln x$ with respect to $x$ (for $x>0$).

Differentiate $y = e^x\,(\ln x)\,\sin(2x)$ with respect to $x$ (for $x>0$).

Differentiate $y = (1+x^2)\,(\ln x)\,\sin x$ with respect to $x$ (for $x>0$).