Differentiate $\ln(5-x)$ with respect to $x$.[1] Differentiate $\frac{1}{\sqrt{x^2+9}}$ with r

Question

Differentiate $\ln(5-x)$ with respect to $x$.[1] Differentiate $\frac{1}{\sqrt{x^2+9}}$ with respect to $x$.[2] Find the exact value of $\displaystyle\int\nolimits_{1}^{2} \left( \frac{1}{\sqrt{x}} + 2x \right)^2 \, \mathrm{d}x.$[5]

Accepted Answer

(a)$-\frac{1}{5-x}$ (b)$-\frac{x}{\sqrt {(x^2+9)^3}}$ (c)$\ln 2 +\frac{16}{3}\sqrt 2+\frac{20}{3}$

2024 RI H1 Q4

2024 RI H1 Q4