Find the derivative of each of the following w.r.t $x$: $y = \frac{\mathrm{e}^{2 - 3x}}{\ln x}$

Question

Find the derivative of each of the following w.r.t $x$: $y = \frac{\mathrm{e}^{2 - 3x}}{\ln x}$ $y = 2\mathrm{e}^{1 - \tan x^{2}}$ $\mathrm{f}(x) = \mathrm{e}^{3x^{5}}\mathrm{e}^{\cos 5x}$

Accepted Answer

(a) $-\frac{e^{2-3x}(3x\ln x+1)}{x(\ln x)^2}$ (b) $-4x\sec^2(x^2)e^{1-\tan(x^2)}$ (c) $(15x^4-5\sin(5x))e^{3x^5+\cos(5x)}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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