Differentiate the following w.r.t x Exercise 1.1
3)Differentiate the following w.r.t x :
(viii)$\frac{1+sin x^{\circ}}{1-sin x^{\circ}}$
Solution-
$\frac{dy}{dx}=\frac{d}{dx}\left(\frac{1+sin x^{\circ}}{1-sin x^{\circ}}\right)$
$=\frac{(1-sin x^{\circ})\frac{dy}{dx}(1+sin x^{\circ})-(1+sin x^{\circ})\frac{d}{dx}(1-sin x^{\circ})}{(1-sin x^{\circ})^2}$
$=\frac{(1-sin x^{\circ})(0+cos x^{\circ})-(1+sin x^{\circ})(0-cos x^{\circ})}{(1-sin x^{\circ})^2}$
$=\frac{(1-sin x^{\circ})cos x^{\circ}-(1+sin x^{\circ})cos x^{\circ}}{(1-sin x^{\circ})^2}$
(i)$(x^2+4x+1)^3+(x^3-5x-2)^4$
(ix)$cot\left(\frac{log x}{2}\right)-log\left(\frac{cot x}{2}\right)$
(x)$\frac{e^{2x}-e^{-2x}}{e^{2x}+e{-2x}}$
(xi)$\frac{e^{\sqrt{x}}+1}{e^{\sqrt{x}}-1}$
(xii)$log\left[ tan^3xsin^4x(x^2+7)\right]$
(xiii)$log\left[\sqrt{\frac{1-cos3x}{1+cos3x}}\right]$
(xiv)$log\left[\sqrt{\frac{1+cos\frac{5x}{2}}{1-cos\frac{5x}{2}}}\right]$
(xv)$log\left[\sqrt{\frac{1-sinx}{1+sinx}}\right]$
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| Differentiate following w.r.t x Exercise 1.1 viii |
