Differentiate with respect to $x$ of the following expressions leaving your answers in terms of \(

Question

Differentiate with respect to $x$ of the following expressions leaving your answers in terms of $x$: $\frac{\sec (\ln x)}{x}$ $\frac{e^{-2x}}{5^x}$ $\ln \sqrt{e^{1+\sec x}}$ $x^\pi$ $\pi^x$ $2^{\ln x}$ $5^{\cos x}$ $x^x$ $(\ln x)^x$

Accepted Answer

(a) $\frac{\sec \left( \ln x ight)\left[ 	an \left( \ln x ight)-1 ight]}{{{x}^{2}}}$ (b) $\frac{{{e}^{-2x}}\left[ \ln 5-2 ight]}{{{5}^{x}}}$ (c) $\frac{1}{2}\ln \left( \sec x+	an x ight)$ (d) $\pi {{x}^{\pi -1}}$ (e) ${{\pi }^{x}}\ln \pi $ (f) $\frac{{{2}^{\ln x}}\ln 2}{x}$ (g) $-\sin x\left( \ln 5 ight){{5}^{\cos x}}$ (h) ${{x}^{x}}\left( 1+\ln x ight)$ (i) ${{\left( \ln x ight)}^{x}}\left[ \frac{1}{\ln x}+\ln \left( \ln x ight) ight]$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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