Advertisements
Advertisements
Question
Find the derivative of x2 – 2 at x = 10.
Advertisements
Solution
= `lim_(h → 0)(f(a + h) - f(a))/h`
∴ Derivative of x2 − 2 at x = 10
= `lim_(h → 0) ([(10 + h)^2 - 2]- (10^2 - 2))/h`
= `lim_(h → 0) (100 + 20h + h^2 - 2 - 100 + 2)/h`
= `lim_(h → 0) (20h + h^2)/h`
= `lim_(h → 0) (20 + h)`
= 20
APPEARS IN
RELATED QUESTIONS
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+ q) (r/s + s)`
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
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):
`(sin x + cos x)/(sin x - cos x)`
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 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):
`(sin(x + a))/ cos x`
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan 2x
\[\sqrt{\tan x}\]
\[\sin \sqrt{2x}\]
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x5 ex + x6 log x
logx2 x
x4 (5 sin x − 3 cos x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
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 of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of 2x4 + x.
`(a + b sin x)/(c + d cos x)`
