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 `2x - 3/4`
Find the derivative of x–3 (5 + 3x).
Find the derivative of x5 (3 – 6x–9).
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):
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):
`cos x/(1 + sin x)`
Find the derivative of f (x) = tan x at x = 0
\[\frac{1}{\sqrt{3 - x}}\]
x2 + x + 3
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
2 sec x + 3 cot x − 4 tan x
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x2 ex log x
sin x cos x
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x4 (5 sin x − 3 cos x)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
(ax + b) (a + d)2
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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 each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
