82. Find the derivative of
$$
f(x)=\frac{x^3+3}{x-1}
$$
83. Find the positive integer n , so that
$$
\lim _{x \rightarrow 3} \frac{x^n-3^n}{x-3}=108
$$
84. Differentiate each of the following functions with respect to x , from first principle.
(i) 15 x
(ii) $$\mathrm{x}^3-1$$
(iii) $$\cos (2 x-3)$$
(iv) $$\sec 3 x$$
(v)12
85. Find the derivative of each of the following functions, with respect to x :
(i) $$\frac{3 x-4 x^3}{x+1}$$
(ii) $$\mathrm{x}^2 \sin \mathrm{x}$$
(iii) $$\left(1-x^2\right)(3 x+4)$$
(iv) $$2 \sin x+3 \cos x$$
(v) $$\frac{3 x+4}{5 x^2-7 x+9}$$
(vi) $$(3 x+7)^3$$
86. For the function $$f$$, given by $$f(x)=x^2-6 x+8$$, prove that $$f^{\prime}(5)-3 f^{\prime}(2)=f^{\prime}(8)$$.
87. Find the derivative of the function $$\mathrm{f}(\mathrm{x})=2 \mathrm{x}^2+3 \mathrm{x}-5$$ at $$\mathrm{x}=-1$$. Also prove that $$\mathrm{f}^{\prime}(0)+3 \mathrm{f}^{\prime}(-1)=0$$.
88. Find the derivative of $$99 x$$ at $$x=100$$.
89. Differentiate each of the following functions, w.r.t.
(i) $$\mathrm{x}^5\left(3-6 \mathrm{x}^{-9}\right)$$
(ii) $$\sin (x+1)$$
90. Find the derivative of $$x^2 \cos x$$.
91. Differentiate each of the following first principal $$x^2 e^x$$.
92. Differentiate each of the following first principal $$e^{\sqrt{a x+b}}$$
93. Differentiate each of the following first principal $$\frac{\cos x}{x}$$
94. Differentiate each of the following first principal $$\sqrt{\sin (3 x+1)}$$.
95. Differentiate each of the following first principal $$\tan (2 x+1)$$.