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 x–3 (5 + 3x).
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):
`cos x/(1 + sin 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:
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
e−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:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan (2x + 1)
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
ex log a + ea long x + ea log a
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x2 ex log x
(x sin x + cos x ) (ex + x2 log x)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(x + 2) (x + 3)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
`(a + b sin x)/(c + d cos x)`
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
