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Find the derivative of x2 – 2 at x = 10.
Let f(x) = x2 – 2. Accordingly,
Thus, the derivative of x2 – 2 at x = 10 is 20.
Find the derivative of x at x = 1.
Let f(x) = x. Accordingly,
Thus, the derivative of x at x = 1 is 1.
Find the derivative of 99x at x = 100.
Let f(x) = 99x. Accordingly,
Thus, the derivative of 99x at x = 100 is 99.
Find the derivative of the following functions from first principle.
(i) x3 – 27 (ii) (x – 1) (x – 2)
(ii) 
(iv) 
(i) Let f(x) = x3 – 27. Accordingly, from the first principle,
(ii) Let f(x) = (x – 1) (x – 2). Accordingly, from the first principle,
(iii) Let
. Accordingly, from the first principle,
(iv) Let
. Accordingly, from the first principle,
For some constants a and b, find the derivative of
(i) (x – a) (x – b) (ii) (ax2 + b)2 (iii) 
(i) Let f (x) = (x – a) (x – b)
(ii) Let 
(iii) 
By quotient rule,
Find the derivative of
(i) 
(ii) (5x3 + 3x – 1) (x – 1)
(iii) x–3 (5 + 3x) (iv) x5 (3 – 6x–9)
(v) x–4 (3 – 4x–5) (vi) 
(i) Let
(ii) Let f (x) = (5x3 + 3x – 1) (x – 1)
By Leibnitz product rule,
(iii) Let f (x) = x– 3 (5 + 3x)
By Leibnitz product rule,
(iv) Let f (x) = x5 (3 – 6x–9)
By Leibnitz product rule,
(v) Let f (x) = x–4 (3 – 4x–5)
By Leibnitz product rule,
(vi) Let f (x) =
By quotient rule,
Find the derivative of cos x from first principle.
Let f (x) = cos x. Accordingly, from the first principle,
Find the derivative of the following functions:
(i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x
(iv) cosec x (v) 3cot x + 5cosec x
(vi) 5sin x – 6cos x + 7 (vii) 2tan x – 7sec x
(i) Let f (x) = sin x cos x. Accordingly, from the first principle,
(ii) Let f (x) = sec x. Accordingly, from the first principle,
(iii) Let f (x) = 5 sec x + 4 cos x. Accordingly, from the first principle,
(iv) Let f (x) = cosec x. Accordingly, from the first principle,
(v) Let f (x) = 3cot x + 5cosec x. Accordingly, from the first principle,
From (1), (2), and (3), we obtain
(vi) Let f (x) = 5sin x – 6cos x + 7. Accordingly, from the first principle,
(vii) Let f (x) = 2 tan x – 7 sec x. Accordingly, from the first principle,
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for some fixed real number a.
for some constant a.
