Question: (a) Differentiate the following function: \(f\left( x \right)=x{{e}^{x}}-{{e}^{x}}\)

(b) Differentiate the following function: \(f\left( x \right)={{5}^{{{x}^{2}}+2x}}\)

(c) Compute \(\int{\frac{\sin \left( {{x}^{1/2}} \right)}{{{x}^{1/2}}}dx}\)

(d) Compute \(\int{\frac{\arcsin x}{\sqrt{1-{{x}^{2}}}}dx}\)

(e) Compute the derivative of \(f\left( x \right)={{\left[ \ln x \right]}^{x}}\)

(f) Differentiate \(f\left( x \right)=\sec \left( \csc x \right)\)

(g) Compute \(\int{\frac{{{e}^{x}}{{\sec }^{2}}\left( {{e}^{x}} \right)}{\tan {{e}^{x}}}dx}\)

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