Differentiate the following with respect to $x$ and simplify your answers. $e^x \cos^2 x$ \(\cos

Question

Differentiate the following with respect to $x$ and simplify your answers. $e^x \cos^2 x$ $\cos^{-1} 3x$ $7^{\ln x}$ $\ln \left( \frac{1 + e^{3x}}{1 - e^{3x}} \right)$

Accepted Answer

(a) ${{e}^{x}}\cos x\left( \cos x-2\sin x \right)$ (b) $-\frac{3}{\sqrt{1-9{{x}^{2}}}}$ (c) $\frac{{{7}^{\ln x}}\ln 7}{x}$ (d) $\frac{6{{e}^{3x}}}{1-{{e}^{6x}}}$

Techniques of Differentiation

Techniques of Differentiation