Let C be a constant. If G(x)=\int_{x}^{e^{x}}\left(\frac{1-\sin t}{t^{2}}+C t\right) d t then what is the derivative of G(x)? G^{\prime}(x)=\frac{e^{x}}{x^{2}}+C x G^{\prime}(x)=\frac{\cos \left(e^{x}\right)}{e^{x}+1}+C G^{\prime}(x)=\left(\frac{1-\sin \left(e^{x}\right)}{\left(e^{x}\right)^{2}}+C e^{x}\right) e^{x}-\frac{1-\sin x}{x^{2}}-C x G^{\prime}(x)=\frac{\left(e^{x}-x\right) \sin

x+\cos x}{x^{2}} G^{\prime}(x)=\frac{\cos x}{x^{2}}+C e^{x}-\frac{\sin \left(e^{x}\right)}{\left(e^{x}\right)^{2}}