Advertisements
Advertisements
प्रश्न
Find the derivative of 2x4 + x.
Advertisements
उत्तर
Let y = 2x4 + x
Differentiating both sides with respect to x, we get
`(dy)/(dx) = d/(dx) (2x^4) + d/(dx) (x)`
= `2 xx 4x^(4 - 1) + 1x^0`
= `8x^3 + 1`
Therefore, `d/(dx) (2x^4 + x) = 8x^3 + 1`.
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
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) (cx + d)2
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 f (x) = 3x at x = 2
Find the derivative of f (x) = 99x at x = 100
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:
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
e3x
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:
\[e^\sqrt{2x}\]
\[\tan \sqrt{x}\]
3x + x3 + 33
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
2 sec x + 3 cot x − 4 tan x
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
(x sin x + cos x ) (ex + x2 log x)
(1 +x2) cos x
sin2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
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
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of x2 cosx.
(ax2 + cot x)(p + q cos x)
