Advertisements
Advertisements
Question
Find the derivative of x at x = 1.
Solution
Let f(x) = x Accordingly,
`f'(1) = lim_(h → 0)(f(1 + h) - f(1))/h`
= ` lim_(h → 0)((1 + h)- 1)/h`
= `lim_(h->0)h/h`
= `lim_(h->0)(1)`
= 1
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
Find the derivative of the following function (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):
`1/(ax^2 + bx + c)`
Find the derivative of the following function (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):
`(px^2 +qx + r)/(ax +b)`
Find the derivative of the following function (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):
(ax + b)n (cx + d)m
Find the derivative of the following function (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):
sinn x
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) x at x = 1
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
\[\frac{x^2 + 1}{x}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
eax + b
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
sin x + cos x
tan2 x
3x + x3 + 33
(2x2 + 1) (3x + 2)
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x3 ex
xn loga x
sin x cos x
x5 ex + x6 log x
logx2 x
x5 (3 − 6x−9)
x−3 (5 + 3x)
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
