Advertisements
Advertisements
प्रश्न
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):
(x + a)
Advertisements
उत्तर
Let f(x) = x + a. Accordingly, f (x + h) = x + h + a
By first principle,
f(x) = `lim_(h->0) (f(x + h) - f(x))/h`
= `lim_(h->0) (x + h + a - x - a)/h`
= `lim_(h->0)(h/h)`
= `lim_(x->0) (1)`
= 1
APPEARS IN
संबंधित प्रश्न
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):
(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):
cosec x cot 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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
x cos x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
(2x2 + 1) (3x + 2)
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
(x3 + x2 + 1) sin x
x2 sin x log x
sin2 x
x4 (5 sin x − 3 cos x)
(ax + b)n (cx + d)n
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
(ax2 + cot x)(p + q cos x)
