LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES1 Mark
Question
Find the derivative of $\frac{x^{5}-\cos x}{\sin x}$
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Answer
Let $h(x)=\frac{x^{5}-\cos x}{\sin x}$ We use the quotient rule on this function wherever it is defined.Then,we have, $h^{\prime}(x)=\frac{\left(x^{5}-\cos x\right)^{\prime} \sin x-\left(x^{5}-\cos x\right)(\sin x)^{\prime}}{(\sin x)^{2}}$ $=\frac{\left(5 x^{4}+\sin x\right) \sin x-\left(x^{5}-\cos x\right) \cos x}{\sin ^{2} x}$ $=\frac{-x^{5} \cos x+5 x^{4} \sin x+1}{(\sin x)^{2}}$
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