Advertisements
Advertisements
Question
(2x2 + 1) (3x + 2)
Solution
\[\frac{d}{dx}\left( \left( 2 x^2 + 1 \right)\left( 3x + 2 \right) \right)\]
\[ = \frac{d}{dx}\left( 6 x^3 + 4 x^2 + 3x + 2 \right)\]
\[ = 6\frac{d}{dx}\left( x^3 \right) + 4\frac{d}{dx}\left( x^2 \right) + 3\frac{d}{dx}\left( x \right) + \frac{d}{dx}\left( 2 \right)\]
\[ = 6\left( 3 x^2 \right) + 4\left( 2x \right) + 3\left( 1 \right) + 0\]
\[ = 18 x^2 + 8x + 3\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
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):
`(ax + b)/(px^2 + qx + r)`
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):
`(sin x + cos x)/(sin x - cos 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 99x at x = 100
\[\frac{1}{x^3}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
x sin 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:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan2 x
\[\sin \sqrt{2x}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x2 ex log x
xn tan x
x5 ex + x6 log x
\[e^x \log \sqrt{x} \tan x\]
x5 (3 − 6x−9)
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)
(ax + b)n (cx + d)n
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Find the derivative of 2x4 + x.
(ax2 + cot x)(p + q cos x)
