Differentiate each of the following with respect to $x$. \(y = \mathrm{e}^{2-3x} - \frac{1}{\mathr

Question

Differentiate each of the following with respect to $x$. $y = \mathrm{e}^{2-3x} - \frac{1}{\mathrm{e}^{x}}$ $y = \sqrt{\mathrm{e}^{x}} + \frac{1}{\sqrt{\mathrm{e}^{x}}}$ $y = \mathrm{e}^{\sqrt{x}}$ $y = \mathrm{e}^{2x^{4}} \mathrm{e}^{6x+1}$

Accepted Answer

(i) $-3\mathrm e^{2-3x}+\mathrm e^{-x}$ (ii) $\dfrac12\mathrm e^{x/2}-\dfrac12\mathrm e^{-x/2}$ (iii) $\dfrac{\mathrm e^{\sqrt{x}}}{2\sqrt{x}}$ (iv) $(8x^3+6)\mathrm e^{2x^4+6x+1}$

Techniques of Differentiation - Derivatives of Exponential Functions

Techniques of Differentiation - Derivatives of Exponential Functions

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