Advertisements
Advertisements
प्रश्न
Find the derivative of f(x) = tan(ax + b), by first principle.
Advertisements
उत्तर
We have f'(x) = `lim_(h -> 0) (f(x + h) - f(x))/h`
= `lim_(h -> 0) (tan(a(x + h) + b) - tan(ax + b))/h`
= `lim_(h -> 0) ((sin(ax + ah + b))/(cos(ax + ah + b)) - (sin(ax + b))/(cos(ax + b)))/h`
= `lim_(h -> 0) (sin(ax + ah + b) cos(ax + b) - sin(ax + b) cos(ax + ah + b))/(h cos(ax + b) cos(ax + ah + b))`
= `lim_(h -> 0) (a sin (ah))/(a * h cos (ax + b) cos(ax + ah + b))`
= `lim_(h -> 0) a/(cos(ax + b) cos(ax + ah + b))`
= `lim_(ah -> 0) (sin ah)/(ah)` ....[as h → 0 ah → 0]
= `a/(cos^2 (ax + b))`
= `a sec^2 (ax + b)`.
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of 99x at x = 100.
Find the derivative of `2x - 3/4`
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):
`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):
sinn x
Find the derivative of f (x) = tan x at x = 0
\[\frac{x + 2}{3x + 5}\]
(x2 + 1) (x − 5)
x ex
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan (2x + 1)
tan 2x
\[\sin \sqrt{2x}\]
2 sec x + 3 cot x − 4 tan x
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
cos (x + a)
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x2 sin x log x
(x sin x + cos x ) (ex + x2 log x)
(1 +x2) cos x
sin2 x
x4 (5 sin x − 3 cos x)
x−4 (3 − 4x−5)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
`(a + b sin x)/(c + d cos x)`
