Question

Find the derivative of $\frac{x^5-cosx}{sinx}$.

• A. $\frac{x^{5}cosx}{si{n}^{2}x}$
• B. $\frac{1}{sinx}-\frac{x^{5}cosx}{si{n}^{2}x}$
• C. $\frac{x}{si{n}^{2}x}$
• D. None of these

Answer 1

Answer: (D)

Let $f\left(x\right)=\frac{x^5-cosx}{sinx}$
$f^{\prime }\left(x\right)=\frac{{\left(x^5-cosx\right)}^{\prime }sinx-\left(x^5-cosx\right){\left(sinx\right)}^{\prime }}{{\left(sinx\right)}^2}$
$\{$using quotient rule$\}$
$=\frac{\left(5x^4+sinx\right)sinx-\left(x^5-cosx\right)cosx}{si{n}^{2}x}$
$=\frac{-x^{5}cosx+5x^{4}sinx+1}{si{n}^{2}x}$