Solution: Let's take $y=\cos \left(\log x+e^{x}\right)$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=-\sin \left(\log x+e^{x}\right) \frac{d}{d x}\left(\log...

Solution: Let's take $y=\frac{\cos x}{\log x}$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=\frac{\log x \frac{d}{d x}(\cos x)-\cos x \frac{d}{d x}(\log x)}{(\log...

Solution: Let's take $y=\log (\log x)$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=\frac{1}{\log x} \frac{d}{d x}(\log x)$ $=\frac{1}{\log x} \cdot...

Solution: Let's take $y=\sqrt{e^{\sqrt{x}}}$ or $\mathrm{y}=\left(e^{\sqrt{x}}\right)^{\frac{1}{2}}$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d...

Solution: Let's take $y=e^{x}+e^{x^{x}}+\ldots . .+e^{x^{x}}$ Now defining the provided function for 5 terms, Now let's say, $y=e^{x}+e^{x^{2}}+e^{x^{3}}+e^{x^{x}}+e^{x^{t}}$ On differentiating the...

Solution: Let's take $y=\log \left(\cos e^{x}\right)$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=\frac{1}{\cos e^{x}} \frac{d}{d x}\left(\cos...

Solution: Let's take $y=\sin \left(\tan ^{-1} e^{-x}\right)$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=\cos \left(\tan ^{-1} e^{-x}\right) \frac{d}{d...

Solution: Let's take $y=e^{x^{3}}=e^{(x)}$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=e^{\left(x^{3}\right)} \frac{d}{d x} x^{3}$ $=e^{\left(x^{3}\right)} \cdot...

Solution: Let's take $y=e^{\operatorname{sin}^{-1} x}$ On differentiating the functions with respect to $x$, we obtain $\frac{d y}{d x}=e^{\operatorname{sin}^{-1} x} \cdot \frac{d}{d x} \sin ^{-1}...

Solution: Let's take $y=\frac{e^{x}}{\sin x}$ On differentiating the functions with respect to $\mathrm{x}$, we obtain $\frac{d y}{d x}=\frac{\sin x \frac{d}{d x} e^{x}-e^{x} \frac{d}{d x} \sin...