List of top Mathematics Questions

For the function f(x) = \(\frac{x^{100}}{100}\) + \(\frac{x^{99}}{99}\) + ......+ \(\frac{x^2}{2}\)+ x+1. Prove that f ′(1)= 100 f'(0 )
Find the derivative of xn + ax n-1 + a2xn-2+……...+a n-1x + an for some fixed real number a.
Expand using Binomial Theorem \(( 1+ \frac{X}{2} - \frac{2}{X})^4, X≠0\)
Find an approximation of (0.99)5 using the first three terms of its expansion
Evaluate\( ( √3 +√2) ^6 - ( √3 -√2) ^6.\)
Find the value of \(( a^2 + \sqrt{a^2-1})^4 + ( a^2 - \sqrt{a^2-1})^4\)
Show that \(9^{ n+1} -8n -9\) is divisible by \(64\), whenever n is a positive integer.
For some constants a and b, find the derivative of
(i) (x-a)(x-b) (ii) (ax2+b)2 (iii)\(\frac{x-a}{x-b}\)
Find the derivative of \(\frac{x^n-a^n}{x-a}\) for some constant a.
Prove that \(\underset{r=0} {\overset{n}∑} { 3^r }\,{ ^nC_r} = 4^n\) 
Find the derivative of
(i) 2x - \(\frac{3}{4}\) 
(ii)(5x3+3x-1)(x-1)
(iii) x-3(5+3x) (iv)x5(3-6x-9)
(v) x-4(3-4x-5) (vi)\(\frac{2}{x+1}-\frac{x^2}{3x-1}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): sin n x

Find the derivative of cos x from first principle.

Find the derivative of the following functions (it is to be understood that \(a, \,b,\, c,\, d,\, p,\, q,\, r\) and \(s\) are fixed non-zero constants and \(m\) and \(n\) are integers), \((x+a)\).

Find the derivative of the following functions:
(i) sin x cos x 
(ii) sec x 
(iii) 5sec x+4cos x
(iv) cosec x 
(v) 3cot x+5cosec x
(vi) 5sin x-6cos x+7 
(vii) 2tan x-7sec x

Find the derivative of the following functions from first principle:
(i) −x (ii) (-x)-1 (iii) sin (x + 1) (iv) cos (x – π/ 8 )
Find the derivative of the following functions from first principle:
(i) −x (ii) (-x)-1 (iii) sin (x + 1) (iv) cos (x – \(\frac{\pi}{8}\))
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax + b) (cx + d)2
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{(ax+b)}{(cx+d)}\)
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\)
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{1}{ax^2+bx+c}\)
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{ax+b}{px^2+qx+r}\)
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{px^2+qx+r}{ax+b}\)
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): 4\(\sqrt x\) -2