Mathematics

Problem

Differentiate the following a.

x \log_e(x^3 + 2)

\sqrt{x} \sin^2 x

\cos^2 \sqrt{\theta}

x^3 e^{-2x^2 + 3}

\cos(x \log_e x)

\log_e(\log_e x)

\frac{x^2 - 4x}{\sin(x^2)}

\frac{10x + 1}{\log_e(10x + 1)}

\frac{\cos(2x)}{e^{1-x}}

x^2 \log_e(\sin 4x)

e^{-\sqrt{x}} \sin \sqrt{x}

\cos(2x \sin x)

\frac{e^{5x+2}}{1-4x}

\frac{\log_e(\sin \theta)}{\cos \theta}

\frac{x}{\sqrt{x+1}}

x \sqrt{x^2 + 2}

(x^3 + x)^3 \sqrt{x+1}

(x^3 - 1) \sqrt{x^3 + 1}

\frac{1}{x} \log_e(x^2 + 1)

\log_e\left(\frac{x^2}{x^2 + 2x}\right)

\frac{\sqrt{x-1}}{x}

e^{-x} \sqrt{x^2 + 9}

(8-x^3) \sqrt{2-x}

x^n \ln(x^n - 1)