Differentiate the following w.r.t x Exercise 1.1
3)Differentiate the following w.r.t x :
(vi)$\sqrt{cos x}+\sqrt{cos\sqrt{x}}$
Solution-
$\frac{dy}{dx}=\frac{d}{dx}\left[(1+sin^2x)^2+(1+cos^2)^3\right]$
$=2(1+sin^2x)\frac{d}{dx}(1+sin^2x)+3(1+cos^2x)^2\frac{d}{dx}(1+cos^2x)$
$=2(1+sin^2x)(0+2sinx\frac{d}{dx}(sinx))+3(1+cosx^2)(0+2cosx\frac{d}{dx}(cosx))$
$=2(1+sin^2x)(2sinxcosx))+3(1+cosx^2)(-2cosxsinx)$
(i)$(x^2+4x+1)^3+(x^3-5x-2)^4$
(iv)$\frac{(x^3-5)^5}{(x^3+5)^3}$
(viii)$\frac{1+sin x^{\circ}}{1-sin x^{\circ}}$
(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 vi |
