Differentiate the function ${\left(a{x}^2+bx+c\right)}^n$ with respect to $x$.

Differentiate $\frac{1}{{\left(x^2-x+3\right)}^3}$ with respect to $x$.

Differentiate ${\sin }^2(2x+3)$ with respect to $x$.

Differentiate ${\cos }^2{x}^3$ with respect to $x$.

Differentiate $\sqrt{\sin \left(x^3\right)}$ with respect to $x$.

Differentiate the function $\sqrt{x \sin x}$ with respect to $x$.

Differentiate $\sqrt{\cot \sqrt{x}}$ with respect to $x$.