Find the derivative of the following functions with respect to $x$: \(\mathrm{f}(x) = e^{\csc x} \

Question

Find the derivative of the following functions with respect to $x$: $\mathrm{f}(x) = e^{\csc x} \cdot 2^{1 - 3x^{2}}$ $y = 3^{\csc 3x}$ $y = \frac{\sin^{2}x}{5^{\cos x}}$

Accepted Answer

(i) $-2^{1-3x^2}e^{\csc x}(6x\ln2+\csc x\cot x)$ (ii) $-3^{1+\csc3x}\ln3\,\csc3x\cot3x$ (iii) $\frac{\sin x(2\cos x+\ln5\sin^2x)}{5^{\cos x}}$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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